I'll solve each equation step by step to find the value of each variable.
1) 4a = 20
Divide both sides by 4: a = 20 ÷ 4 = 5 ✓ (already given)
2) b - 7 = 8
Add 7 to both sides: b = 8 + 7 = 15
3) 2c - 1 = 11
Add 1 to both sides: 2c = 12
Divide by 2: c = 6
4) 10 = d + 6
Subtract 6 from both sides: d = 10 - 6 = 4
5) 18 = 3e
Divide both sides by 3: e = 18 ÷ 3 = 6
6) f - 7 = 4 + 4
Simplify right side: f - 7 = 8
Add 7 to both sides: f = 8 + 7 = 15
7) 2g = 7 - 5
Simplify right side: 2g = 2
Divide by 2: g = 1
8) 16 - 2h = 0
Subtract 16 from both sides: -2h = -16
Divide by -2: h = 8
9) 2(i + 1) = 18
Divide both sides by 2: i + 1 = 9
Subtract 1: i = 8
10) 3(j - 1) = 21
Divide both sides by 3: j - 1 = 7
Add 1: j = 8
11) 5(k + 2) = 45
Divide both sides by 5: k + 2 = 9
Subtract 2: k = 7
12) 4(l - 6) = 16
Divide both sides by 4: l - 6 = 4
Add 6: l = 10
13) 2m - 5 = 11
Add 5 to both sides: 2m = 16
Divide by 2: m = 8
14) ½n + 1 = 8
Subtract 1 from both sides: ½n = 7
Multiply by 2: n = 14
15) 20 ÷ o = 4
This means 20/o = 4, so o = 20 ÷ 4 = 5
16) p ÷ 7 = 3
Multiply both sides by 7: p = 3 × 7 = 21
17) q/6 = 5
Multiply both sides by 6: q = 5 × 6 = 30
18) 4(r + 2) = 24
Divide both sides by 4: r + 2 = 6
Subtract 2: r = 4
19) 20 = 5(s - 3)
Divide both sides by 5: 4 = s - 3
Add 3: s = 7
20) ½t + 7 = 13
Subtract 7 from both sides: ½t = 6
Multiply by 2: t = 12
21) u² = 36
Take square root: u = ±6 (both positive and negative work)
22) v² = 100
Take square root: v = ±10 (both positive and negative work)
23) w = √25
w = 5 (principal square root is positive)
24) 3x = 20 - 8
Simplify right side: 3x = 12
Divide by 3: x = 4
25) 18 - 4y = 2
Subtract 18 from both sides: -4y = -16
Divide by -4: y = 4
Final Answer:
b=15, c=6, d=4, e=6, f=15, g=1, h=8, i=8, j=8, k=7, l=10, m=8, n=14, o=5, p=21, q=30, r=4, s=7, t=12, u=±6, v=±10, w=5, x=4, y=4
Parent Tip: Review the logic above to help your child master the concept of solving simple equations worksheet.
