Question

which of the following equations have the same solution? move the blue rectangles to select two correct answers. 8 - x = 56 - 5x 0.5x - 3 = -2x + 7 11x + 6 = 3x + 8 9x = 24 + 7x 57 = 12 + 5x

Explanation:

Step1: Solve $8 - x=56 - 5x$

Add $5x$ to both sides: $8 - x+5x=56 - 5x+5x$, which simplifies to $8 + 4x=56$. Then subtract 8 from both sides: $4x=56 - 8=48$, and $x = 12$.

Step2: Solve $0.5x-3=-2x + 7$

Add $2x$ to both sides: $0.5x+2x-3=-2x+2x + 7$, so $2.5x-3=7$. Add 3 to both sides: $2.5x=7 + 3=10$, and $x = 4$.

Step3: Solve $11x + 6=3x+8$

Subtract $3x$ from both sides: $11x-3x + 6=3x-3x+8$, getting $8x+6=8$. Subtract 6 from both sides: $8x=8 - 6=2$, and $x=\frac{1}{4}$.

Step4: Solve $9x=24 + 7x$

Subtract $7x$ from both sides: $9x-7x=24+7x-7x$, so $2x=24$, and $x = 12$.

Step5: Solve $57=12 + 5x$

Subtract 12 from both sides: $57-12=12-12 + 5x$, getting $45=5x$, and $x = 9$.

Answer:

$8 - x=56 - 5x$, $9x=24 + 7x$