Math  /  Algebra

Question1) 3x=2x+503 x=2 x+50 2) 6x=2x+446 x=2 x+44 3) 8x=2x+368 x=2 x+36 4) 4x=x+184 x=x+18 3x=2x+503x2x+50\begin{array}{l} 3 x=2 x+50 \\ 3 x \neq 2 x+50 \end{array}

Studdy Solution

STEP 1

1. Each equation is a linear equation in one variable.
2. We are solving for x x in each equation.
3. Basic algebraic manipulation is used to isolate x x .

STEP 2

1. Solve equation 1: 3x=2x+50 3x = 2x + 50 .
2. Solve equation 2: 6x=2x+44 6x = 2x + 44 .
3. Solve equation 3: 8x=2x+36 8x = 2x + 36 .
4. Solve equation 4: 4x=x+18 4x = x + 18 .
5. Analyze the inequality 3x2x+50 3x \neq 2x + 50 .

STEP 3

To solve the equation 3x=2x+50 3x = 2x + 50 , subtract 2x 2x from both sides to isolate x x :
3x2x=50 3x - 2x = 50
x=50 x = 50

STEP 4

To solve the equation 6x=2x+44 6x = 2x + 44 , subtract 2x 2x from both sides to isolate x x :
6x2x=44 6x - 2x = 44
4x=44 4x = 44
Divide both sides by 4:
x=444 x = \frac{44}{4}
x=11 x = 11

STEP 5

To solve the equation 8x=2x+36 8x = 2x + 36 , subtract 2x 2x from both sides to isolate x x :
8x2x=36 8x - 2x = 36
6x=36 6x = 36
Divide both sides by 6:
x=366 x = \frac{36}{6}
x=6 x = 6

STEP 6

To solve the equation 4x=x+18 4x = x + 18 , subtract x x from both sides to isolate x x :
4xx=18 4x - x = 18
3x=18 3x = 18
Divide both sides by 3:
x=183 x = \frac{18}{3}
x=6 x = 6

STEP 7

Analyze the inequality 3x2x+50 3x \neq 2x + 50 :
Subtract 2x 2x from both sides:
3x2x50 3x - 2x \neq 50
x50 x \neq 50
This indicates that x x cannot be equal to 50.
The solutions to the equations are: 1) x=50 x = 50 2) x=11 x = 11 3) x=6 x = 6 4) x=6 x = 6
The inequality 3x2x+50 3x \neq 2x + 50 implies x50 x \neq 50 .

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