Let’s solve each problem one by one, step by step. We’ll isolate the variable (x or y) on one side of the equation.
---
1.
$\frac{y}{5} + 11 = 13$
Subtract 11 from both sides:
$\frac{y}{5} = 2$
Multiply both sides by 5:
$y = 10$
---
2.
$\frac{x}{6} + 10 = 12$
Subtract 10 from both sides:
$\frac{x}{6} = 2$
Multiply both sides by 6:
$x = 12$
---
3.
$\frac{11 + 10}{y + 6} = 3$
Simplify numerator:
$\frac{21}{y + 6} = 3$
Multiply both sides by $y + 6$:
$21 = 3(y + 6)$
Divide both sides by 3:
$7 = y + 6$
Subtract 6:
$y = 1$
---
4.
$11 + (7 \times x + 1) - 1 + (8 \times x) = 146$
Remove parentheses and combine like terms:
$11 + 7x + 1 - 1 + 8x = 146$
Combine constants: $11 + 1 - 1 = 11$
Combine x terms: $7x + 8x = 15x$
So:
$15x + 11 = 146$
Subtract 11:
$15x = 135$
Divide by 15:
$x = 9$
---
5.
$\frac{11}{y} = 1$
Multiply both sides by y:
$11 = y$
So:
$y = 11$
---
6.
$10 \times (8 + y) = 190$
Divide both sides by 10:
$8 + y = 19$
Subtract 8:
$y = 11$
---
7.
$\frac{x}{12} + 7 = 7$
Subtract 7 from both sides:
$\frac{x}{12} = 0$
Multiply by 12:
$x = 0$
---
8.
$6 \times (5 - y) = -18$
Divide both sides by 6:
$5 - y = -3$
Subtract 5 from both sides:
$-y = -8$
Multiply both sides by -1:
$y = 8$
---
9.
$8 + \frac{y}{11} = 8$
Subtract 8 from both sides:
$\frac{y}{11} = 0$
Multiply by 11:
$y = 0$
---
10.
$\frac{7 + 11}{x + 4} = 2$
Simplify numerator:
$\frac{18}{x + 4} = 2$
Multiply both sides by $x + 4$:
$18 = 2(x + 4)$
Divide both sides by 2:
$9 = x + 4$
Subtract 4:
$x = 5$
---
Final Answer:
1. y = 10
2. x = 12
3. y = 1
4. x = 9
5. y = 11
6. y = 11
7. x = 0
8. y = 8
9. y = 0
10. x = 5
Parent Tip: Review the logic above to help your child master the concept of algebra worksheet 7 6.
