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3 years ago

Solve for X. Each figure is a parallelogram.

Mathematics

1 answer:

vichka [17]3 years ago

7 0

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

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

84 + 16x = 180

84 - 84 + 16x = 180 - 84

16x = 96

16x/16 = 96/16

x = 6

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

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

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

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