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The problem asks to solve the following equations: 1) $3a - 7 = 26$ 2) $9f + 5 = 77$ 3) $2k - 20 = 40$ 4) $6b - 4 = 38$ 5) $10h + 58 = -2$ 6) $-4d + 17 = 65$ 7) $8m + 11 = -53$ 8) $5z - 1.75 = 8.25$ 9) $\frac{1}{2}n + 40 = 55$ 10) $-\frac{1}{4}c - 5 = 20$ 11) $4.8g + 9 = 33$ 12) $\frac{1}{3}p + 22 = 18$ 13) $1.2y + 0.52 = 7$ 14) $2.5t + 24 = 14$ 15) $5j + \frac{2}{3} = -\frac{1}{3}$

AlgebraLinear EquationsSolving Equations
2025/4/8

1. Problem Description

The problem asks to solve the following equations:
1) 3a−7=263a - 7 = 26
2) 9f+5=779f + 5 = 77
3) 2k−20=402k - 20 = 40
4) 6b−4=386b - 4 = 38
5) 10h+58=−210h + 58 = -2
6) −4d+17=65-4d + 17 = 65
7) 8m+11=−538m + 11 = -53
8) 5z−1.75=8.255z - 1.75 = 8.25
9) 12n+40=55\frac{1}{2}n + 40 = 55
10) −14c−5=20-\frac{1}{4}c - 5 = 20
11) 4.8g+9=334.8g + 9 = 33
12) 13p+22=18\frac{1}{3}p + 22 = 18
13) 1.2y+0.52=71.2y + 0.52 = 7
14) 2.5t+24=142.5t + 24 = 14
15) 5j+23=−135j + \frac{2}{3} = -\frac{1}{3}

2. Solution Steps

1) 3a−7=263a - 7 = 26
Add 7 to both sides: 3a=26+7=333a = 26 + 7 = 33
Divide by 3: a=333=11a = \frac{33}{3} = 11
2) 9f+5=779f + 5 = 77
Subtract 5 from both sides: 9f=77−5=729f = 77 - 5 = 72
Divide by 9: f=729=8f = \frac{72}{9} = 8
3) 2k−20=402k - 20 = 40
Add 20 to both sides: 2k=40+20=602k = 40 + 20 = 60
Divide by 2: k=602=30k = \frac{60}{2} = 30
4) 6b−4=386b - 4 = 38
Add 4 to both sides: 6b=38+4=426b = 38 + 4 = 42
Divide by 6: b=426=7b = \frac{42}{6} = 7
5) 10h+58=−210h + 58 = -2
Subtract 58 from both sides: 10h=−2−58=−6010h = -2 - 58 = -60
Divide by 10: h=−6010=−6h = \frac{-60}{10} = -6
6) −4d+17=65-4d + 17 = 65
Subtract 17 from both sides: −4d=65−17=48-4d = 65 - 17 = 48
Divide by -4: d=48−4=−12d = \frac{48}{-4} = -12
7) 8m+11=−538m + 11 = -53
Subtract 11 from both sides: 8m=−53−11=−648m = -53 - 11 = -64
Divide by 8: m=−648=−8m = \frac{-64}{8} = -8
8) 5z−1.75=8.255z - 1.75 = 8.25
Add 1.75 to both sides: 5z=8.25+1.75=105z = 8.25 + 1.75 = 10
Divide by 5: z=105=2z = \frac{10}{5} = 2
9) 12n+40=55\frac{1}{2}n + 40 = 55
Subtract 40 from both sides: 12n=55−40=15\frac{1}{2}n = 55 - 40 = 15
Multiply by 2: n=15∗2=30n = 15 * 2 = 30
10) −14c−5=20-\frac{1}{4}c - 5 = 20
Add 5 to both sides: −14c=20+5=25-\frac{1}{4}c = 20 + 5 = 25
Multiply by -4: c=25∗−4=−100c = 25 * -4 = -100
11) 4.8g+9=334.8g + 9 = 33
Subtract 9 from both sides: 4.8g=33−9=244.8g = 33 - 9 = 24
Divide by 4.8: g=244.8=24048=5g = \frac{24}{4.8} = \frac{240}{48} = 5
12) 13p+22=18\frac{1}{3}p + 22 = 18
Subtract 22 from both sides: 13p=18−22=−4\frac{1}{3}p = 18 - 22 = -4
Multiply by 3: p=−4∗3=−12p = -4 * 3 = -12
13) 1.2y+0.52=71.2y + 0.52 = 7
Subtract 0.52 from both sides: 1.2y=7−0.52=6.481.2y = 7 - 0.52 = 6.48
Divide by 1.2: y=6.481.2=64.812=5.4y = \frac{6.48}{1.2} = \frac{64.8}{12} = 5.4
14) 2.5t+24=142.5t + 24 = 14
Subtract 24 from both sides: 2.5t=14−24=−102.5t = 14 - 24 = -10
Divide by 2.5: t=−102.5=−4t = \frac{-10}{2.5} = -4
15) 5j+23=−135j + \frac{2}{3} = -\frac{1}{3}
Subtract 23\frac{2}{3} from both sides: 5j=−13−23=−33=−15j = -\frac{1}{3} - \frac{2}{3} = -\frac{3}{3} = -1
Divide by 5: j=−15=−15j = \frac{-1}{5} = -\frac{1}{5}

3. Final Answer

1) a=11a = 11
2) f=8f = 8
3) k=30k = 30
4) b=7b = 7
5) h=−6h = -6
6) d=−12d = -12
7) m=−8m = -8
8) z=2z = 2
9) n=30n = 30
10) c=−100c = -100
11) g=5g = 5
12) p=−12p = -12
13) y=5.4y = 5.4
14) t=−4t = -4
15) j=−15j = -\frac{1}{5}

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