Answer:
1. x = 8
2. x = 3
3. x = 25
4. x = 6
5. x = 11
6. x = 3
7. x = 6
8. x = 10
Step-by-step explanation:
Since the opposite sides of a parallelogram are congruent, the length of segment QR is equal to the length of segment PS.
10 = -6 + 2x
Add 6 to each side
10 + 6 = -6 + 6 + 2x
Simplify each side
16 = 2x
Divide both sides by 2
16/2 = 2x/2
Simplify
x = 8
to check if x is correct:
you already know that segment QR is 10, so your answer needs to be equal to 10
so sement PS is -6x + 2x
-6 + 2x
= -6 + 2(8)
= -6 + 16
= 10
so PS = 10
2. 34x + 5 = 35x + 2
Step 1: Subtract 35x from both sides.
34x + 5 − 35x = 35x + 2 − 35x
−x + 5 = 2
Step 2: Subtract 5 from both sides.
−x + 5 − 5 = 2 − 5
−x = −3
Step 3: Divide both sides by -1.
-x/-1 = -3/-1
Step 4: Simplify
x = 3
3.
115 = 2x + 65
Step 1: Flip the equation.
2x + 65 = 115
Step 2: Subtract 65 from both sides.
2x + 65 − 65 = 115 − 65
2x = 50
Step 3: Divide both sides by 2.
2x/2 = 50/2
x = 25
4.
84 + 16x = 180
84 - 84 + 16x = 180 - 84
16x = 96
16x/16 = 96/16
x = 6
5.
2(3x − 10) = 46
Step 1: Simplify both sides of the equation.
2(3x − 10) = 46
(2)(3x) + (2)(−10 )= 46(Distribute)
6x + −20 = 46
6x − 20 = 46
Step 2: Add 20 to both sides.
6x − 20 + 20 = 46 + 20
6x = 66
Step 3: Divide both sides by 6.
6x/6 = 66/6
x = 11
6. RH = 1/2 FH or RH = 2 × FH
Step 1: Simplify both sides of the equation.
(2)(12)=13x−2
24=13x+−2
24=13x−2
Step 2: Flip the equation.
13x−2=24
Step 3: Add 2 to both sides.
13x−2+2=24+2
13x=26
Step 4: Divide both sides by 13.
13x/13 = 26/13
x = 3
7.
2x+2=3x−4
Step 1: Subtract 3x from both sides.
2x+2−3x=3x−4−3x
−x+2=−4
Step 2: Subtract 2 from both sides.
−x+2−2=−4−2
−x=−6
Step 3: Divide both sides by -1.
-x/-1 = -6/-1
x = 6
8.
2(2x−6)=28
Step 1: Simplify both sides of the equation.
2(2x−6)=28
(2)(2x)+(2)(−6)=28(Distribute)
4x+−12=28
4x−12=28
Step 2: Add 12 to both sides.
4x−12+12=28+12
4x=40
Step 3: Divide both sides by 4.
4x/4 = 40/4
x = 10
