Question Match each linear equation with an equivalent equation. Some choices are not used. A. $3x+6=4x+7$ B. $3(x+6)=4x+7$ C. $4x+3x=7-6$

Studdy Solution

STEP 1

Assumptions
1. We are given three equations labeled A, B, and C.
2. We are given five possible equivalent equations labeled 1 to 5.
3. We need to match each of the given equations A, B, and C with one of the equivalent equations 1 to 5.
4. Some of the answer choices may not be used, indicating that there may be unmatched equations.
5. Equivalent equations have the same solution set.

STEP 2

Begin by simplifying equation A if possible to see if it matches any of the given equivalent equations.
$3x + 6 = 4x + 7$

STEP 3

To simplify equation A, we can try to isolate the variable $x$ on one side. We can do this by subtracting $3x$ from both sides of the equation.
$3x + 6 - 3x = 4x + 7 - 3x$

STEP 4

Simplify both sides of the equation after subtracting $3x$ .
$6 = x + 7$

STEP 5

Now, subtract 7 from both sides to isolate $x$ .
$6 - 7 = x + 7 - 7$

STEP 6

Simplify both sides of the equation after subtracting 7.
$-1 = x$

STEP 7

We have simplified equation A to $x = -1$ . Now we need to find an equivalent equation among the choices 1 to 5 that simplifies to $x = -1$ . We can see that choice 4, $3x - 1 = 4x$ , simplifies to $x = -1$ when we subtract $3x$ from both sides.
$3x - 1 - 3x = 4x - 3x$ $-1 = x$
Thus, equation A matches with equivalent equation 4.

STEP 8

Next, simplify equation B if possible to see if it matches any of the given equivalent equations.
$3(x + 6) = 4x + 7$

STEP 9

To simplify equation B, distribute the 3 on the left side of the equation.
$3x + 18 = 4x + 7$

STEP 10

We can see that the simplified form of equation B, $3x + 18 = 4x + 7$ , matches exactly with choice 2.
Thus, equation B matches with equivalent equation 2.

STEP 11

Finally, simplify equation C if possible to see if it matches any of the given equivalent equations.
$4x + 3x = 7 - 6$

STEP 12

Combine like terms on the left side of equation C.
$7x = 7 - 6$

STEP 13

Simplify the right side of equation C.
$7x = 1$

STEP 14

We can see that the simplified form of equation C, $7x = 1$ , matches exactly with choice 5.
Thus, equation C matches with equivalent equation 5.

STEP 15

Now we have matched all three given equations with their equivalent equations:
- Equation A matches with equivalent equation 4. - Equation B matches with equivalent equation 2. - Equation C matches with equivalent equation 5.

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Question Match each linear equation with an equivalent equation. Some choices are not used. A. $3x+6=4x+7$ B. $3(x+6)=4x+7$ C. $4x+3x=7-6$

Studdy Solution

STEP 1

STEP 2

Begin by simplifying equation A if possible to see if it matches any of the given equivalent equations.
$3x + 6 = 4x + 7$

STEP 3

To simplify equation A, we can try to isolate the variable $x$ on one side. We can do this by subtracting $3x$ from both sides of the equation.
$3x + 6 - 3x = 4x + 7 - 3x$

STEP 4

Simplify both sides of the equation after subtracting $3x$ .
$6 = x + 7$

STEP 5

Now, subtract 7 from both sides to isolate $x$ .
$6 - 7 = x + 7 - 7$

STEP 6

Simplify both sides of the equation after subtracting 7.
$-1 = x$

STEP 7

STEP 8

Next, simplify equation B if possible to see if it matches any of the given equivalent equations.
$3(x + 6) = 4x + 7$

STEP 9

To simplify equation B, distribute the 3 on the left side of the equation.
$3x + 18 = 4x + 7$

STEP 10

We can see that the simplified form of equation B, $3x + 18 = 4x + 7$ , matches exactly with choice 2.
Thus, equation B matches with equivalent equation 2.

STEP 11

Finally, simplify equation C if possible to see if it matches any of the given equivalent equations.
$4x + 3x = 7 - 6$

STEP 12

Combine like terms on the left side of equation C.
$7x = 7 - 6$

STEP 13

Simplify the right side of equation C.
$7x = 1$

STEP 14

We can see that the simplified form of equation C, $7x = 1$ , matches exactly with choice 5.
Thus, equation C matches with equivalent equation 5.

STEP 15

Now we have matched all three given equations with their equivalent equations:
- Equation A matches with equivalent equation 4. - Equation B matches with equivalent equation 2. - Equation C matches with equivalent equation 5.

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Question Match each linear equation with an equivalent equation. Some choices are not used. A. 3x+6=4x+73x+6=4x+73x+6=4x+7 B. 3(x+6)=4x+73(x+6)=4x+73(x+6)=4x+7 C. 4x+3x=7−64x+3x=7-64x+3x=7−6

Studdy Solution

STEP 1

STEP 2

Begin by simplifying equation A if possible to see if it matches any of the given equivalent equations.3x+6=4x+73x + 6 = 4x + 73x+6=4x+7

STEP 3

To simplify equation A, we can try to isolate the variable xxx on one side. We can do this by subtracting 3x3x3x from both sides of the equation.3x+6−3x=4x+7−3x3x + 6 - 3x = 4x + 7 - 3x3x+6−3x=4x+7−3x

STEP 4

Simplify both sides of the equation after subtracting 3x3x3x.6=x+76 = x + 76=x+7

STEP 5

Now, subtract 7 from both sides to isolate xxx.6−7=x+7−76 - 7 = x + 7 - 76−7=x+7−7

STEP 6

Simplify both sides of the equation after subtracting 7.−1=x-1 = x−1=x

STEP 7

STEP 8

Next, simplify equation B if possible to see if it matches any of the given equivalent equations.3(x+6)=4x+73(x + 6) = 4x + 73(x+6)=4x+7

STEP 9

To simplify equation B, distribute the 3 on the left side of the equation.3x+18=4x+73x + 18 = 4x + 73x+18=4x+7

STEP 10

We can see that the simplified form of equation B, 3x+18=4x+73x + 18 = 4x + 73x+18=4x+7, matches exactly with choice 2.Thus, equation B matches with equivalent equation 2.

STEP 11

Finally, simplify equation C if possible to see if it matches any of the given equivalent equations.4x+3x=7−64x + 3x = 7 - 64x+3x=7−6

STEP 12

Combine like terms on the left side of equation C.7x=7−67x = 7 - 67x=7−6

STEP 13

Simplify the right side of equation C.7x=17x = 17x=1

STEP 14

We can see that the simplified form of equation C, 7x=17x = 17x=1, matches exactly with choice 5.Thus, equation C matches with equivalent equation 5.

STEP 15

Now we have matched all three given equations with their equivalent equations:- Equation A matches with equivalent equation 4. - Equation B matches with equivalent equation 2. - Equation C matches with equivalent equation 5.

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Question Match each linear equation with an equivalent equation. Some choices are not used. A. $3x+6=4x+7$ B. $3(x+6)=4x+7$ C. $4x+3x=7-6$

Begin by simplifying equation A if possible to see if it matches any of the given equivalent equations.
$3x + 6 = 4x + 7$

To simplify equation A, we can try to isolate the variable $x$ on one side. We can do this by subtracting $3x$ from both sides of the equation.
$3x + 6 - 3x = 4x + 7 - 3x$

Simplify both sides of the equation after subtracting $3x$ .
$6 = x + 7$

Now, subtract 7 from both sides to isolate $x$ .
$6 - 7 = x + 7 - 7$

Simplify both sides of the equation after subtracting 7.
$-1 = x$

Next, simplify equation B if possible to see if it matches any of the given equivalent equations.
$3(x + 6) = 4x + 7$

To simplify equation B, distribute the 3 on the left side of the equation.
$3x + 18 = 4x + 7$

We can see that the simplified form of equation B, $3x + 18 = 4x + 7$ , matches exactly with choice 2.
Thus, equation B matches with equivalent equation 2.

Finally, simplify equation C if possible to see if it matches any of the given equivalent equations.
$4x + 3x = 7 - 6$

Combine like terms on the left side of equation C.
$7x = 7 - 6$

Simplify the right side of equation C.
$7x = 1$

We can see that the simplified form of equation C, $7x = 1$ , matches exactly with choice 5.
Thus, equation C matches with equivalent equation 5.

Now we have matched all three given equations with their equivalent equations:
- Equation A matches with equivalent equation 4. - Equation B matches with equivalent equation 2. - Equation C matches with equivalent equation 5.