Question

solving multi-step equations
directions : show all work on a separate piece of paper.
circle the answer choice that represents the correct answer.
then use the color choice to color the picture.

	question	choice a	choice b	choice c
2	$-5x + 5x + 2x - 6x - 12x = -16$	$x = 1$ green	$x = -1$ orange	$x = 16$ blue
3	$3(x - 6) = 6$	$x = 4$ black	$x = -4$ pink	$x = 8$ yellow
4	$-9 - x - 7x = 7 - 10x$	$x = -8$ blue	$x = 8$ purple	$x = 18$ red
5	$10 + 4x = 6x - 10$	$x = 10$ blue	$x = -10$ black	$x = -2$ green
6	$7x = 8x - 3$	$x = 5$ pink	$x = 3$ orange	$x = -3$ black
7	$-6x - 10 = 10 - 10x$	$x = -5$ gray	$x = 5$ pink	$x = 10$ black
8	$-8x = -7x + 10$	$x = -10$ green	$x = 10$ blue	$x = 25$ orange
9	$-2x + 6 = -x$	$x = -6$ blue	$x = -8$ black	$x = 6$ yellow
10	$2(x + 8) + -8 = -6$	$x = 7$ white	$x = -7$ pink	$x = 17$ purple
11	$3x + 30 = 14x + 140$	$x = 5$ orange	$x = 20$ red	$x = -10$ blue
12	$65x - 50 = 40x + 150$	$x = 40$ yellow	$x = 5$ pink	$x = 8$ purple

Explanation:

Step1: Solve the equation \(5x - 4x = 15\)

Simplify the left side: \(5x - 4x = x\), so the equation becomes \(x = 15\).

Step2: Solve the equation \(-5x + 5x + 2x - 6x - 12x = -16\)

Combine like terms: \((-5x + 5x)+(2x - 6x - 12x)=0+( - 16x)= - 16x\), so \(-16x=-16\), divide both sides by -16: \(x = 1\).

Step3: Solve the equation \(3(x - 6)=6\)

Distribute the 3: \(3x-18 = 6\), add 18 to both sides: \(3x=6 + 18=24\), divide by 3: \(x = 8\).

Step4: Solve the equation \(-9 - x - 7x = 7 - 10x\)

Combine like terms on left: \(-9-8x = 7 - 10x\), add \(10x\) to both sides: \(-9 + 2x=7\), add 9 to both sides: \(2x=16\), divide by 2: \(x = 8\)? Wait, no, let's re - do: \(-9-8x=7 - 10x\), add \(10x\) to both sides: \(-9 + 2x=7\), add 9: \(2x=16\), \(x = 8\)? But the option A is \(x=-8\), maybe I made a mistake. Wait, original equation: \(-9 - x - 7x=7 - 10x\), left side: \(-9-8x\), right side: \(7 - 10x\). Add \(10x\) to both sides: \(-9 + 2x=7\), add 9: \(2x = 16\), \(x = 8\). But the option A is \(x=-8\), maybe the user's marked answer is wrong, but according to calculation, \(x = 8\). Wait, maybe I misread the equation. Let me check again: \(-9 - x - 7x=7 - 10x\), \(-9-8x=7 - 10x\), add \(10x\): \(-9 + 2x=7\), \(2x=16\), \(x = 8\). But the marked answer is A (\(x=-8\) BLUE). Maybe a typo, but following the calculation steps as per the problem's requirement to solve.

Step5: Solve the equation \(10 + 4x = 6x - 10\)

Subtract \(4x\) from both sides: \(10=2x - 10\), add 10: \(20 = 2x\), divide by 2: \(x = 10\).

Step6: Solve the equation \(7x = 8x - 3\)

Subtract \(7x\) from both sides: \(0=x - 3\), add 3: \(x = 3\)? Wait, \(7x=8x - 3\), subtract \(8x\): \(-x=-3\), so \(x = 3\).

Step7: Solve the equation \(-6x - 10 = 10 - 10x\)

Add \(10x\) to both sides: \(4x-10 = 10\), add 10: \(4x=20\), divide by 4: \(x = 5\).

Step8: Solve the equation \(-8x=-7x + 10\)

Add \(7x\) to both sides: \(-x = 10\), multiply by -1: \(x=-10\).

Step9: Solve the equation \(-2x + 6=-x\)

Add \(2x\) to both sides: \(6=x\), so \(x = 6\).

Step10: Solve the equation \(2(x + 8)-8=-6\)

Distribute: \(2x+16 - 8=-6\), simplify: \(2x + 8=-6\), subtract 8: \(2x=-14\), divide by 2: \(x=-7\).

Step11: Solve the equation \(3x + 30 = 14x + 140\)

Subtract \(3x\): \(30 = 11x+140\), subtract 140: \(-110 = 11x\), divide by 11: \(x=-10\).

Step12: Solve the equation \(65x - 50 = 40x + 150\)

Subtract \(40x\): \(25x-50 = 150\), add 50: \(25x=200\), divide by 25: \(x = 8\).

Answer:

1. \(x = 15\) (Choice A)
2. \(x = 1\) (Choice A)
3. \(x = 8\) (Choice C)
4. Let's re - solve: \(-9 - x - 7x=7 - 10x\)

\(-9-8x=7 - 10x\)
\(-8x + 10x=7 + 9\)
\(2x=16\)
\(x = 8\) (But marked as A, maybe error)

1. \(x = 10\) (Choice A)
2. \(7x=8x - 3\)

\(8x-7x = 3\)
\(x = 3\) (Choice B)

1. \(x = 5\) (Choice B)
2. \(x=-10\) (Choice A)
3. \(x = 6\) (Choice C)
4. \(x=-7\) (Choice B)
5. \(x=-10\) (Choice C)
6. \(x = 8\) (Choice C)

(Note: Some of the marked answers in the image may have calculation errors based on the standard solving of linear equations.)