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Solve Two-Step Inequalities (px + q > r)

Students solve inequalities of the form px + q > r or px + q < r, graph the solution on a number line, and interpret the solution in context. They understand that multiplying or dividing by a negative number reverses the inequality sign.

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Solve Two-Step Inequalities (px + q > r)

Grade 7 · Expressions and Equations · question 1 of 3

0 of 20

20 rungs. A star at the top.

−7x + 14 < −42, x >

How it is taught

0:00 of 4:12

An inequality compares two sides with greater than or less than.

The solution set is every number that makes it true.

Read it: Two-step equations and inequalities

4x + 12 = 36 is a tape: 4 equal parts of x and 12 more make 36. Take the 12 away: 4x = 24. Share 24 into 4 equal parts: x = 6.

  1. Undo the last move on x first: − 12 undoes + 12, and ÷ 3 undoes × 3.
  2. Then share what is left into the equal parts: divide both sides.
  3. Check by putting x back in: 4 × 6 + 12 = 36.

Each undo is done to both sides, so the two sides stay equal: 36 − 12 = 24, and 24 ÷ 4 = 6.

An inequality is undone the same way, but dividing both sides by a negative number turns the sign: −2x < 12 becomes x > −6.

x < 6 is every number less than 6: an open circle at 6, because 6 itself is not a solution, and a ray to the left.

Undo in reverse order, on both sides. Dividing an inequality by a negative number turns its sign.

Dividing 4x and 36 by 4 but not the 12: x + 12 = 9, so x = −3.

Take the 12 away first: 4x = 24. Then 24 ÷ 4 = 6, so x = 6.

7x + 18 < 95, x < ___ — 11. Take 18 away from both sides: 7x < 77. Then 77 ÷ 7 = 11, so x < 11.

2x + 3 > 11

Maya saves three dollars, then earns two dollars for every chore. How many chores does she need to have MORE than eleven dollars?

We can write that as two x plus three is greater than eleven.

Our goal is to get x by itself. First, let's undo the plus three.

Subtract three from BOTH sides to keep the inequality balanced.

That leaves two x is greater than eight.

Now undo the times two. Since two is positive, the sign stays the same.

Divide both sides by two.

x is greater than four!

Let's show our answer on a number line.

Put an OPEN circle on four — open, because four itself is not a solution.

Then shade to the right, for every number bigger than four.

x is greater than four. Maya needs five or more chores. Great work!

Maya needs MORE than $11$3 saved · $2 per chore · how many chores?2x + 3>11− 3− 32x>8÷ positive → sign stays!÷ 2÷ 2x>408012345678open at 4ANSWERx > 45+ chores
Grade 7 · Solve 2x + 3 > 11 and graph the solution

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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