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Math  /  Algebra

QuestionSolve. a) x+9=15x+9=15 b) p−10=13p-10=13 c) 8x=248 x=24 d) 6y=−306 y=-30 e) −9=k+7-9=k+7 f) −4h=28-4 h=28 g) x+(−3)=9x+(-3)=9 h) −4x=−32-4 x=-32 i) −8+x=−17-8+x=-17 j) y−(−12)=−18y-(-12)=-18 k) 16=2x16=2 x 1) −19=−12+c-19=-12+c

Studdy Solution

STEP 1

1. Each equation involves a single variable and requires basic algebraic operations to solve.
2. The goal is to isolate the variable on one side of the equation.
3. We will check each solution by substituting it back into the original equation.

STEP 2

1. Isolate the variable for each equation.
2. Solve for the variable.
3. Check the solution by substituting it back into the original equation.

STEP 3

Equation a) x+9=15 x + 9 = 15
Subtract 9 from both sides to isolate x x :
x=15−9 x = 15 - 9

STEP 4

Simplify:
x=6 x = 6

STEP 5

Check the solution by substituting back:
6+9=15 6 + 9 = 15
The solution is correct.

STEP 6

Equation b) p−10=13 p - 10 = 13
Add 10 to both sides to isolate p p :
p=13+10 p = 13 + 10

STEP 7

Simplify:
p=23 p = 23

STEP 8

Check the solution by substituting back:
23−10=13 23 - 10 = 13
The solution is correct.

STEP 9

Equation c) 8x=24 8x = 24
Divide both sides by 8 to isolate x x :
x=248 x = \frac{24}{8}

STEP 10

Simplify:
x=3 x = 3

STEP 11

Check the solution by substituting back:
8×3=24 8 \times 3 = 24
The solution is correct.

STEP 12

Equation d) 6y=−30 6y = -30
Divide both sides by 6 to isolate y y :
y=−306 y = \frac{-30}{6}

STEP 13

Simplify:
y=−5 y = -5

STEP 14

Check the solution by substituting back:
6×(−5)=−30 6 \times (-5) = -30
The solution is correct.

STEP 15

Equation e) −9=k+7 -9 = k + 7
Subtract 7 from both sides to isolate k k :
k=−9−7 k = -9 - 7

STEP 16

Simplify:
k=−16 k = -16

STEP 17

Check the solution by substituting back:
−16+7=−9 -16 + 7 = -9
The solution is correct.

STEP 18

Equation f) −4h=28 -4h = 28
Divide both sides by -4 to isolate h h :
h=28−4 h = \frac{28}{-4}

STEP 19

Simplify:
h=−7 h = -7

STEP 20

Check the solution by substituting back:
−4×(−7)=28 -4 \times (-7) = 28
The solution is correct.

STEP 21

Equation g) x+(−3)=9 x + (-3) = 9
Add 3 to both sides to isolate x x :
x=9+3 x = 9 + 3

STEP 22

Simplify:
x=12 x = 12

STEP 23

Check the solution by substituting back:
12+(−3)=9 12 + (-3) = 9
The solution is correct.

STEP 24

Equation h) −4x=−32 -4x = -32
Divide both sides by -4 to isolate x x :
x=−32−4 x = \frac{-32}{-4}

STEP 25

Simplify:
x=8 x = 8

STEP 26

Check the solution by substituting back:
−4×8=−32 -4 \times 8 = -32
The solution is correct.

STEP 27

Equation i) −8+x=−17 -8 + x = -17
Add 8 to both sides to isolate x x :
x=−17+8 x = -17 + 8

STEP 28

Simplify:
x=−9 x = -9

STEP 29

Check the solution by substituting back:
−8+(−9)=−17 -8 + (-9) = -17
The solution is correct.

STEP 30

Equation j) y−(−12)=−18 y - (-12) = -18
Add 12 to both sides to isolate y y :
y=−18+12 y = -18 + 12

STEP 31

Simplify:
y=−6 y = -6

STEP 32

Check the solution by substituting back:
−6−(−12)=−18 -6 - (-12) = -18
The solution is correct.

STEP 33

Equation k) 16=2x 16 = 2x
Divide both sides by 2 to isolate x x :
x=162 x = \frac{16}{2}

STEP 34

Simplify:
x=8 x = 8

STEP 35

Check the solution by substituting back:
2×8=16 2 \times 8 = 16
The solution is correct.

STEP 36

Equation l) −19=−12+c -19 = -12 + c
Add 12 to both sides to isolate c c :
c=−19+12 c = -19 + 12

STEP 37

Simplify:
c=−7 c = -7

STEP 38

Check the solution by substituting back:
−12+(−7)=−19 -12 + (-7) = -19
The solution is correct.

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