Question

unit: solving equations and inequalities progress: question id: 1177336 the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. match each equation on the left with its solution on the right. no answer on the right will be used twice. 3x + 2(x - 4) = 4(x - 1) + x 4x + 2(x - 4) = 8(x - 1) - 2x 3x + 2(x - 4) = 4(x - 1) - x 4x + 2(x - 4) = 4(x - 2) + x x = 2 no solution all real numbers x = 0 clear click and hold an item in one column, then drag it to the matching item in the other column. be sure your cursor is over the target before releasing. the target will highlight or the cursor will change. need help? watch this video.

Explanation:

Step1: Expand both sides

$3x + 2x - 8 = 4x - 4 + x$

Step2: Combine like terms

$5x - 8 = 5x - 4$

Step3: Isolate variable terms

$5x - 5x = -4 + 8$
$0 = 4$

Conclusion for first equation: No solution

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Step1: Expand both sides

$4x + 2x - 8 = 8x - 8 - 2x$

Step2: Combine like terms

$6x - 8 = 6x - 8$

Step3: Simplify equation

$6x - 6x = -8 + 8$
$0 = 0$

Conclusion for second equation: All real numbers

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Step1: Expand both sides

$3x + 2x - 8 = 4x - 4 - x$

Step2: Combine like terms

$5x - 8 = 3x - 4$

Step3: Isolate variable terms

$5x - 3x = -4 + 8$
$2x = 4$

Step4: Solve for x

$x = \frac{4}{2} = 2$

Conclusion for third equation: $x=2$

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Step1: Expand both sides

$4x + 2x - 8 = 4x - 8 + x$

Step2: Combine like terms

$6x - 8 = 5x - 8$

Step3: Isolate variable terms

$6x - 5x = -8 + 8$
$x = 0$

Conclusion for fourth equation: $x=0$

Answer:

• $3x + 2(x - 4) = 4(x - 1) + x$ → No solution
• $4x + 2(x - 4) = 8(x - 1) - 2x$ → All real numbers
• $3x + 2(x - 4) = 4(x - 1) - x$ → $x = 2$
• $4x + 2(x - 4) = 4(x - 2) + x$ → $x = 0$