Math  /  Geometry

QuestionWrite and solve an inequality to find the values of xx for which the perimeter of the rectangle is less than 14

Studdy Solution

STEP 1

1. The rectangle has sides of length xx and x+4x + 4.
2. The perimeter of the rectangle is less than 14.

STEP 2

1. Recall the formula for the perimeter of a rectangle.
2. Write the inequality for the perimeter.
3. Solve the inequality for xx.

STEP 3

Recall the formula for the perimeter of a rectangle:
P=2×(Length+Width) P = 2 \times (\text{Length} + \text{Width})

STEP 4

Write the inequality for the perimeter being less than 14:
2×(x+(x+4))<14 2 \times (x + (x + 4)) < 14

STEP 5

Simplify and solve the inequality:
2×(x+x+4)<14 2 \times (x + x + 4) < 14 2×(2x+4)<14 2 \times (2x + 4) < 14 4x+8<14 4x + 8 < 14
Subtract 8 from both sides:
4x<6 4x < 6
Divide both sides by 4:
x<64 x < \frac{6}{4} x<32 x < \frac{3}{2}
The values of xx for which the perimeter is less than 14 are:
x<32 x < \frac{3}{2}

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord