Algebra 1 Worksheets | Equations Worksheets - Free Printable

Here are the step-by-step solutions for each equation.

1) $2(2.5 + 8.5a) = -28.5$
* Step 1: Distribute the 2 into the parentheses: $2 \times 2.5 = 5$ and $2 \times 8.5a = 17a$.
Equation becomes: $5 + 17a = -28.5$
* Step 2: Subtract 5 from both sides: $17a = -28.5 - 5$
$17a = -33.5$
* Step 3: Divide by 17: $a = -33.5 / 17$
$a \approx -1.9705...$
* Rounding: Round to the nearest hundredth: -1.97

2) $7(9c + 6) = 20.5 + 9.5c$
* Step 1: Distribute the 7: $63c + 42 = 20.5 + 9.5c$
* Step 2: Subtract $9.5c$ from both sides to group the variables: $53.5c + 42 = 20.5$
* Step 3: Subtract 42 from both sides: $53.5c = 20.5 - 42$
$53.5c = -21.5$
* Step 4: Divide by 53.5: $c = -21.5 / 53.5$
$c \approx -0.4018...$
* Rounding: Round to the nearest hundredth: -0.40

3) $-5.5 + 3.5(1 - 9.5z) = 25.5$
* Step 1: Distribute the 3.5: $3.5 \times 1 = 3.5$ and $3.5 \times -9.5z = -33.25z$.
Equation becomes: $-5.5 + 3.5 - 33.25z = 25.5$
* Step 2: Combine like terms on the left ($-5.5 + 3.5 = -2$):
$-2 - 33.25z = 25.5$
* Step 3: Add 2 to both sides: $-33.25z = 27.5$
* Step 4: Divide by -33.25: $z = 27.5 / -33.25$
$z \approx -0.8270...$
* Rounding: Round to the nearest hundredth: -0.83

4) $-3(1 + 4.5r) = -17.5$
* Step 1: Distribute the -3: $-3 - 13.5r = -17.5$
* Step 2: Add 3 to both sides: $-13.5r = -14.5$
* Step 3: Divide by -13.5: $r = -14.5 / -13.5$
$r \approx 1.0740...$
* Rounding: Round to the nearest hundredth: 1.07

5) $4.5v - 3v = 24.5$
* Step 1: Combine like terms on the left side ($4.5 - 3 = 1.5$):
$1.5v = 24.5$
* Step 2: Divide by 1.5: $v = 24.5 / 1.5$
$v \approx 16.3333...$
* Rounding: Round to the nearest hundredth: 16.33

6) $-26.5 = 8f - 9f$
* Step 1: Combine like terms on the right side ($8f - 9f = -1f$ or just $-f$):
$-26.5 = -f$
* Step 2: Multiply or divide by -1 to isolate f:
$f = 26.5$
* Answer: 26.5 (No rounding needed)

7) $-18.5 = 8 + 6(k - 7.5)$
* Step 1: Distribute the 6: $6 \times k = 6k$ and $6 \times -7.5 = -45$.
Equation becomes: $-18.5 = 8 + 6k - 45$
* Step 2: Combine constants on the right ($8 - 45 = -37$):
$-18.5 = 6k - 37$
* Step 3: Add 37 to both sides: $18.5 = 6k$
* Step 4: Divide by 6: $k = 18.5 / 6$
$k \approx 3.0833...$
* Rounding: Round to the nearest hundredth: 3.08

8) $-2(3n + 9) = 30.5$
* Step 1: Distribute the -2: $-6n - 18 = 30.5$
* Step 2: Add 18 to both sides: $-6n = 48.5$
* Step 3: Divide by -6: $n = 48.5 / -6$
$n \approx -8.0833...$
* Rounding: Round to the nearest hundredth: -8.08

9) $19.5 = 2.5(7.5y - 9.5)$
* Step 1: Distribute the 2.5: $2.5 \times 7.5y = 18.75y$ and $2.5 \times -9.5 = -23.75$.
Equation becomes: $19.5 = 18.75y - 23.75$
* Step 2: Add 23.75 to both sides: $43.25 = 18.75y$
* Step 3: Divide by 18.75: $y = 43.25 / 18.75$
$y \approx 2.3066...$
* Rounding: Round to the nearest hundredth: 2.31

10) $5s + 3.5 + 6s = 26.5$
* Step 1: Combine like terms on the left ($5s + 6s = 11s$):
$11s + 3.5 = 26.5$
* Step 2: Subtract 3.5 from both sides: $11s = 23$
* Step 3: Divide by 11: $s = 23 / 11$
$s \approx 2.0909...$
* Rounding: Round to the nearest hundredth: 2.09

Final Answer:
1) a = -1.97
2) c = -0.40
3) z = -0.83
4) r = 1.07
5) v = 16.33
6) f = 26.5
7) k = 3.08
8) n = -8.08
9) y = 2.31
10) s = 2.09