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Math  /  Algebra

Question5. 54=135−x54=135-x
6. z−7=−19z-7=-19
7.  Exit ficket z−9=−15\begin{array}{l}\text { Exit ficket } \\ z-9=-15\end{array}
8. 52=12−b52=12-b
9. −67=c−(−4)-67=c-(-4)
10. x−7=87x-7=87

Studdy Solution

STEP 1

1. Each equation involves solving for a single variable.
2. The equations require basic algebraic operations such as addition, subtraction, multiplication, or division.
3. The goal is to isolate the variable on one side of the equation.

STEP 2

1. Solve the equation for the variable.
2. Check the solution by substituting it back into the original equation.
**Problem 5: 54=135−x 54 = 135 - x **

STEP 3

To isolate x x , subtract 135 from both sides:
54−135=−x 54 - 135 = -x

STEP 4

Simplify the left side:
−81=−x -81 = -x

STEP 5

Multiply both sides by −1-1 to solve for x x :
x=81 x = 81

STEP 6

Check the solution by substituting x=81 x = 81 back into the original equation:
54=135−81 54 = 135 - 81
Simplify the right side:
54=54 54 = 54
The solution is correct.
**Problem 6: z−7=−19 z - 7 = -19 **
STEP_1: Add 7 to both sides to isolate z z :
z=−19+7 z = -19 + 7
STEP_2: Simplify the right side:
z=−12 z = -12
STEP_3: Check the solution by substituting z=−12 z = -12 back into the original equation:
−12−7=−19 -12 - 7 = -19
Simplify the left side:
−19=−19 -19 = -19
The solution is correct.
**Problem 7: z−9=−15 z - 9 = -15 **
STEP_1: Add 9 to both sides to isolate z z :
z=−15+9 z = -15 + 9
STEP_2: Simplify the right side:
z=−6 z = -6
STEP_3: Check the solution by substituting z=−6 z = -6 back into the original equation:
−6−9=−15 -6 - 9 = -15
Simplify the left side:
−15=−15 -15 = -15
The solution is correct.
**Problem 8: 52=12−b 52 = 12 - b **
STEP_1: Subtract 12 from both sides to isolate −b-b:
52−12=−b 52 - 12 = -b
STEP_2: Simplify the left side:
40=−b 40 = -b
STEP_3: Multiply both sides by −1-1 to solve for b b :
b=−40 b = -40
STEP_4: Check the solution by substituting b=−40 b = -40 back into the original equation:
52=12−(−40) 52 = 12 - (-40)
Simplify the right side:
52=52 52 = 52
The solution is correct.
**Problem 9: −67=c−(−4) -67 = c - (-4) **
STEP_1: Simplify the right side by changing the subtraction of a negative to addition:
−67=c+4 -67 = c + 4
STEP_2: Subtract 4 from both sides to isolate c c :
−67−4=c -67 - 4 = c
STEP_3: Simplify the left side:
−71=c -71 = c
STEP_4: Check the solution by substituting c=−71 c = -71 back into the original equation:
−67=−71−(−4) -67 = -71 - (-4)
Simplify the right side:
−67=−67 -67 = -67
The solution is correct.
**Problem 10: x−7=87 x - 7 = 87 **
STEP_1: Add 7 to both sides to isolate x x :
x=87+7 x = 87 + 7
STEP_2: Simplify the right side:
x=94 x = 94
STEP_3: Check the solution by substituting x=94 x = 94 back into the original equation:
94−7=87 94 - 7 = 87
Simplify the left side:
87=87 87 = 87
The solution is correct.

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