Math / Algebra

QuestionSolve the equation graphically. Check your solution algebraically.
1. $5 x+2=7$
2. $-3 x=15$ (3.) $2-x=5$ $y=5 x+2$ $y=2 x$ $y=5$ $y=7$ $\frac{2 x}{2}=\frac{5}{2}$ $\left(1=\frac{5}{2}\right.$
4. $8+2 x=-2 x$ (5.) $0.5 x+1=3$
6. $3 x+6=11-2$

Studdy Solution

STEP 1

1. We need to solve each equation graphically and then verify the solution algebraically.
2. For graphical solutions, we will plot the equations and find the intersection points.
3. For algebraic verification, we will solve the equations using algebraic methods.

STEP 2

1. Solve the equation $5x + 2 = 7$ graphically and check algebraically.
2. Solve the equation $-3x = 15$ graphically and check algebraically.
3. Solve the equation $2 - x = 5$ graphically and check algebraically.
4. Solve the equation $8 + 2x = -2x$ graphically and check algebraically.
5. Solve the equation $0.5x + 1 = 3$ graphically and check algebraically.
6. Solve the equation $3x + 6 = 11 - 2$ graphically and check algebraically.

STEP 3

Graphically solve $5x + 2 = 7$ : - Plot the line $y = 5x + 2$ . - Plot the line $y = 7$ . - Find the intersection point of the two lines.

STEP 4

Algebraically solve $5x + 2 = 7$ : - Subtract 2 from both sides: $5x = 5$ . - Divide both sides by 5: $x = 1$ .
Check: - Substitute $x = 1$ back into the original equation: $5(1) + 2 = 7$ . - Verify: $7 = 7$ .

STEP 5

Graphically solve $-3x = 15$ : - Plot the line $y = -3x$ . - Plot the line $y = 15$ . - Find the intersection point of the two lines.

STEP 6

Algebraically solve $-3x = 15$ : - Divide both sides by -3: $x = -5$ .
Check: - Substitute $x = -5$ back into the original equation: $-3(-5) = 15$ . - Verify: $15 = 15$ .

STEP 7

Graphically solve $2 - x = 5$ : - Plot the line $y = 2 - x$ . - Plot the line $y = 5$ . - Find the intersection point of the two lines.

STEP 8

Algebraically solve $2 - x = 5$ : - Subtract 2 from both sides: $-x = 3$ . - Multiply both sides by -1: $x = -3$ .
Check: - Substitute $x = -3$ back into the original equation: $2 - (-3) = 5$ . - Verify: $5 = 5$ .

STEP 9

Graphically solve $8 + 2x = -2x$ : - Plot the line $y = 8 + 2x$ . - Plot the line $y = -2x$ . - Find the intersection point of the two lines.

STEP 10

Algebraically solve $8 + 2x = -2x$ : - Add $2x$ to both sides: $8 + 4x = 0$ . - Subtract 8 from both sides: $4x = -8$ . - Divide both sides by 4: $x = -2$ .
Check: - Substitute $x = -2$ back into the original equation: $8 + 2(-2) = -2(-2)$ . - Verify: $4 = 4$ .

STEP 11

Graphically solve $0.5x + 1 = 3$ : - Plot the line $y = 0.5x + 1$ . - Plot the line $y = 3$ . - Find the intersection point of the two lines.

STEP 12

Algebraically solve $0.5x + 1 = 3$ : - Subtract 1 from both sides: $0.5x = 2$ . - Divide both sides by 0.5: $x = 4$ .
Check: - Substitute $x = 4$ back into the original equation: $0.5(4) + 1 = 3$ . - Verify: $3 = 3$ .

STEP 13

Graphically solve $3x + 6 = 11 - 2$ : - Simplify the right side: $3x + 6 = 9$ . - Plot the line $y = 3x + 6$ . - Plot the line $y = 9$ . - Find the intersection point of the two lines.

STEP 14

Algebraically solve $3x + 6 = 9$ : - Subtract 6 from both sides: $3x = 3$ . - Divide both sides by 3: $x = 1$ .
Check: - Substitute $x = 1$ back into the original equation: $3(1) + 6 = 11 - 2$ . - Verify: $9 = 9$ .

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QuestionSolve the equation graphically. Check your solution algebraically.
1. $5 x+2=7$
2. $-3 x=15$ (3.) $2-x=5$ $y=5 x+2$ $y=2 x$ $y=5$ $y=7$ $\frac{2 x}{2}=\frac{5}{2}$ $\left(1=\frac{5}{2}\right.$
4. $8+2 x=-2 x$ (5.) $0.5 x+1=3$
6. $3 x+6=11-2$

Studdy Solution

STEP 1

1. We need to solve each equation graphically and then verify the solution algebraically.
2. For graphical solutions, we will plot the equations and find the intersection points.
3. For algebraic verification, we will solve the equations using algebraic methods.

STEP 2

STEP 3

Graphically solve $5x + 2 = 7$ : - Plot the line $y = 5x + 2$ . - Plot the line $y = 7$ . - Find the intersection point of the two lines.

STEP 4

Algebraically solve $5x + 2 = 7$ : - Subtract 2 from both sides: $5x = 5$ . - Divide both sides by 5: $x = 1$ .
Check: - Substitute $x = 1$ back into the original equation: $5(1) + 2 = 7$ . - Verify: $7 = 7$ .

STEP 5

Graphically solve $-3x = 15$ : - Plot the line $y = -3x$ . - Plot the line $y = 15$ . - Find the intersection point of the two lines.

STEP 6

Algebraically solve $-3x = 15$ : - Divide both sides by -3: $x = -5$ .
Check: - Substitute $x = -5$ back into the original equation: $-3(-5) = 15$ . - Verify: $15 = 15$ .

STEP 7

Graphically solve $2 - x = 5$ : - Plot the line $y = 2 - x$ . - Plot the line $y = 5$ . - Find the intersection point of the two lines.

STEP 8

Algebraically solve $2 - x = 5$ : - Subtract 2 from both sides: $-x = 3$ . - Multiply both sides by -1: $x = -3$ .
Check: - Substitute $x = -3$ back into the original equation: $2 - (-3) = 5$ . - Verify: $5 = 5$ .

STEP 9

Graphically solve $8 + 2x = -2x$ : - Plot the line $y = 8 + 2x$ . - Plot the line $y = -2x$ . - Find the intersection point of the two lines.

STEP 10

Algebraically solve $8 + 2x = -2x$ : - Add $2x$ to both sides: $8 + 4x = 0$ . - Subtract 8 from both sides: $4x = -8$ . - Divide both sides by 4: $x = -2$ .
Check: - Substitute $x = -2$ back into the original equation: $8 + 2(-2) = -2(-2)$ . - Verify: $4 = 4$ .

STEP 11

Graphically solve $0.5x + 1 = 3$ : - Plot the line $y = 0.5x + 1$ . - Plot the line $y = 3$ . - Find the intersection point of the two lines.

STEP 12

Algebraically solve $0.5x + 1 = 3$ : - Subtract 1 from both sides: $0.5x = 2$ . - Divide both sides by 0.5: $x = 4$ .
Check: - Substitute $x = 4$ back into the original equation: $0.5(4) + 1 = 3$ . - Verify: $3 = 3$ .

STEP 13

Graphically solve $3x + 6 = 11 - 2$ : - Simplify the right side: $3x + 6 = 9$ . - Plot the line $y = 3x + 6$ . - Plot the line $y = 9$ . - Find the intersection point of the two lines.

STEP 14

Algebraically solve $3x + 6 = 9$ : - Subtract 6 from both sides: $3x = 3$ . - Divide both sides by 3: $x = 1$ .
Check: - Substitute $x = 1$ back into the original equation: $3(1) + 6 = 11 - 2$ . - Verify: $9 = 9$ .

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Studdy Solution

STEP 1

1. We need to solve each equation graphically and then verify the solution algebraically.2. For graphical solutions, we will plot the equations and find the intersection points.3. For algebraic verification, we will solve the equations using algebraic methods.

STEP 2

STEP 3

Graphically solve 5x+2=75x + 2 = 75x+2=7: - Plot the line y=5x+2y = 5x + 2y=5x+2. - Plot the line y=7y = 7y=7. - Find the intersection point of the two lines.

STEP 4

Algebraically solve 5x+2=75x + 2 = 75x+2=7: - Subtract 2 from both sides: 5x=55x = 55x=5. - Divide both sides by 5: x=1x = 1x=1.Check: - Substitute x=1x = 1x=1 back into the original equation: 5(1)+2=75(1) + 2 = 75(1)+2=7. - Verify: 7=77 = 77=7.

STEP 5

Graphically solve −3x=15-3x = 15−3x=15: - Plot the line y=−3xy = -3xy=−3x. - Plot the line y=15y = 15y=15. - Find the intersection point of the two lines.

STEP 6

Algebraically solve −3x=15-3x = 15−3x=15: - Divide both sides by -3: x=−5x = -5x=−5.Check: - Substitute x=−5x = -5x=−5 back into the original equation: −3(−5)=15-3(-5) = 15−3(−5)=15. - Verify: 15=1515 = 1515=15.

STEP 7

Graphically solve 2−x=52 - x = 52−x=5: - Plot the line y=2−xy = 2 - xy=2−x. - Plot the line y=5y = 5y=5. - Find the intersection point of the two lines.

STEP 8

Algebraically solve 2−x=52 - x = 52−x=5: - Subtract 2 from both sides: −x=3-x = 3−x=3. - Multiply both sides by -1: x=−3x = -3x=−3.Check: - Substitute x=−3x = -3x=−3 back into the original equation: 2−(−3)=52 - (-3) = 52−(−3)=5. - Verify: 5=55 = 55=5.

STEP 9

Graphically solve 8+2x=−2x8 + 2x = -2x8+2x=−2x: - Plot the line y=8+2xy = 8 + 2xy=8+2x. - Plot the line y=−2xy = -2xy=−2x. - Find the intersection point of the two lines.

STEP 10

STEP 11

Graphically solve 0.5x+1=30.5x + 1 = 30.5x+1=3: - Plot the line y=0.5x+1y = 0.5x + 1y=0.5x+1. - Plot the line y=3y = 3y=3. - Find the intersection point of the two lines.

STEP 12

Algebraically solve 0.5x+1=30.5x + 1 = 30.5x+1=3: - Subtract 1 from both sides: 0.5x=20.5x = 20.5x=2. - Divide both sides by 0.5: x=4x = 4x=4.Check: - Substitute x=4x = 4x=4 back into the original equation: 0.5(4)+1=30.5(4) + 1 = 30.5(4)+1=3. - Verify: 3=33 = 33=3.

STEP 13

Graphically solve 3x+6=11−23x + 6 = 11 - 23x+6=11−2: - Simplify the right side: 3x+6=93x + 6 = 93x+6=9. - Plot the line y=3x+6y = 3x + 6y=3x+6. - Plot the line y=9y = 9y=9. - Find the intersection point of the two lines.

STEP 14

Algebraically solve 3x+6=93x + 6 = 93x+6=9: - Subtract 6 from both sides: 3x=33x = 33x=3. - Divide both sides by 3: x=1x = 1x=1.Check: - Substitute x=1x = 1x=1 back into the original equation: 3(1)+6=11−23(1) + 6 = 11 - 23(1)+6=11−2. - Verify: 9=99 = 99=9.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. We need to solve each equation graphically and then verify the solution algebraically.
2. For graphical solutions, we will plot the equations and find the intersection points.
3. For algebraic verification, we will solve the equations using algebraic methods.

Graphically solve $5x + 2 = 7$ : - Plot the line $y = 5x + 2$ . - Plot the line $y = 7$ . - Find the intersection point of the two lines.

Algebraically solve $5x + 2 = 7$ : - Subtract 2 from both sides: $5x = 5$ . - Divide both sides by 5: $x = 1$ .
Check: - Substitute $x = 1$ back into the original equation: $5(1) + 2 = 7$ . - Verify: $7 = 7$ .

Graphically solve $-3x = 15$ : - Plot the line $y = -3x$ . - Plot the line $y = 15$ . - Find the intersection point of the two lines.

Algebraically solve $-3x = 15$ : - Divide both sides by -3: $x = -5$ .
Check: - Substitute $x = -5$ back into the original equation: $-3(-5) = 15$ . - Verify: $15 = 15$ .

Graphically solve $2 - x = 5$ : - Plot the line $y = 2 - x$ . - Plot the line $y = 5$ . - Find the intersection point of the two lines.

Algebraically solve $2 - x = 5$ : - Subtract 2 from both sides: $-x = 3$ . - Multiply both sides by -1: $x = -3$ .
Check: - Substitute $x = -3$ back into the original equation: $2 - (-3) = 5$ . - Verify: $5 = 5$ .

Graphically solve $8 + 2x = -2x$ : - Plot the line $y = 8 + 2x$ . - Plot the line $y = -2x$ . - Find the intersection point of the two lines.

Graphically solve $0.5x + 1 = 3$ : - Plot the line $y = 0.5x + 1$ . - Plot the line $y = 3$ . - Find the intersection point of the two lines.

Algebraically solve $0.5x + 1 = 3$ : - Subtract 1 from both sides: $0.5x = 2$ . - Divide both sides by 0.5: $x = 4$ .
Check: - Substitute $x = 4$ back into the original equation: $0.5(4) + 1 = 3$ . - Verify: $3 = 3$ .

Graphically solve $3x + 6 = 11 - 2$ : - Simplify the right side: $3x + 6 = 9$ . - Plot the line $y = 3x + 6$ . - Plot the line $y = 9$ . - Find the intersection point of the two lines.

Algebraically solve $3x + 6 = 9$ : - Subtract 6 from both sides: $3x = 3$ . - Divide both sides by 3: $x = 1$ .
Check: - Substitute $x = 1$ back into the original equation: $3(1) + 6 = 11 - 2$ . - Verify: $9 = 9$ .