We read your photo as:

Solve the inequality $-7 < 5x − 2 "; Represent the solution on a real number line.

Mathematics

ScanSolve AI Answer

Answer

a

−1<x≤1-1 < x \le 1

Step-by-step solution

2 steps

Here's the solution for the inequality:

:

Part a· 2 steps

Solve the inequality −7<5x−2≤3-7 < 5x - 2 \le 3.

  1. Add 2 to all three parts of the inequality to isolate the term with xx.

    −7+2<5x−2+2≤3+2-7 + 2 < 5x - 2 + 2 \le 3 + 2 −5<5x≤5-5 < 5x \le 5
  2. Divide all three parts by 5 to solve for xx.

    −55<5x5≤55\frac{-5}{5} < \frac{5x}{5} \le \frac{5}{5} −1<x≤1-1 < x \le 1

    The solution is −1<x≤1-1 < x \le 1.

    −1<x≤1\boxed{-1 < x \le 1}

Part b

Represent the solution of (a) on a real number line.

To represent −1<x≤1-1 < x \le 1 on a real number line, draw a number line. Place an open circle at −1-1 (because xx is strictly greater than −1-1). Place a closed circle (or a filled dot) at 1 (because xx is less than or equal to 1). Draw a line segment connecting these two circles, indicating that all numbers between −1-1 and 1 (including 1 but not −1-1) are part of the solution.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp