Question

worksheet
name:
instructions: solve each equation for the variable. show all of your work.

1. 5x + 3x - 10 = 38
2. -4y + 12 - 7y=-1
3. 9 - 2m+6m = 45
4. 21a + 43a - 5 = 20
5. 6.5z - 1.5z+14 = 34
6. 3(p + 5)-7 = 29
7. -5(2k - 4)+1 = 61
8. 4(w - 9)+2w = 0

Explanation:

Step1: Combine like - terms

1. For the equation \(5x + 3x-10 = 38\), combine the \(x\) - terms: \((5 + 3)x-10=38\), which simplifies to \(8x-10 = 38\).
2. Add 10 to both sides: \(8x-10 + 10=38 + 10\), so \(8x=48\).
3. Divide both sides by 8: \(\frac{8x}{8}=\frac{48}{8}\), and \(x = 6\).

Step2: Combine like - terms

For the equation \(-4y+12 - 7y=-1\), combine the \(y\) - terms: \((-4-7)y+12=-1\), which simplifies to \(-11y+12=-1\).
Subtract 12 from both sides: \(-11y+12 - 12=-1 - 12\), so \(-11y=-13\).
Divide both sides by \(-11\): \(y=\frac{13}{11}\).

Step3: Combine like - terms

For the equation \(9-2m + 6m=45\), combine the \(m\) - terms: \((-2 + 6)m+9=45\), which simplifies to \(4m+9=45\).
Subtract 9 from both sides: \(4m+9 - 9=45 - 9\), so \(4m=36\).
Divide both sides by 4: \(m = 9\).

Step4: Combine like - terms

For the equation \(21a+43a-5=20\), combine the \(a\) - terms: \((21 + 43)a-5=20\), which simplifies to \(64a-5=20\).
Add 5 to both sides: \(64a-5 + 5=20+5\), so \(64a=25\).
Divide both sides by 64: \(a=\frac{25}{64}\).

Step5: Combine like - terms

For the equation \(6.5z-1.5z+14=34\), combine the \(z\) - terms: \((6.5 - 1.5)z+14=34\), which simplifies to \(5z+14=34\).
Subtract 14 from both sides: \(5z+14 - 14=34 - 14\), so \(5z=20\).
Divide both sides by 5: \(z = 4\).

Step6: Expand and simplify

For the equation \(3(p + 5)-7=29\), first expand \(3(p + 5)\) to get \(3p+15\).
The equation becomes \(3p+15-7=29\), then \(3p + 8=29\).
Subtract 8 from both sides: \(3p+8 - 8=29 - 8\), so \(3p=21\).
Divide both sides by 3: \(p = 7\).

Step7: Expand and simplify

For the equation \(-5(2k-4)+1=61\), first expand \(-5(2k - 4)\) to get \(-10k + 20\).
The equation becomes \(-10k+20 + 1=61\), then \(-10k+21=61\).
Subtract 21 from both sides: \(-10k+21 - 21=61 - 21\), so \(-10k=40\).
Divide both sides by \(-10\): \(k=-4\).

Step8: Expand and simplify

For the equation \(4(w - 9)+2w=0\), first expand \(4(w - 9)\) to get \(4w-36\).
The equation becomes \(4w-36+2w=0\), then combine like - terms: \((4 + 2)w-36=0\), so \(6w-36=0\).
Add 36 to both sides: \(6w-36 + 36=0 + 36\), so \(6w=36\).
Divide both sides by 6: \(w = 6\).

Answer:

1. \(x = 6\)
2. \(y=\frac{13}{11}\)
3. \(m = 9\)
4. \(a=\frac{25}{64}\)
5. \(z = 4\)
6. \(p = 7\)
7. \(k=-4\)
8. \(w = 6\)