Solving Multistep Inequalities

-2(5 + 6n) < 6(8 − 2n)

• no solution

• infinite solution

• x < 0

• x > 0

You want to spend at most $1200 on a new laptop.  If you make a $400 down payment, then pay the same amount every month for 12 months.  Which Inequality could be use to solve to find out how much you can pay each month.

• 12x + 1200 > 400

• 12x + 400 < 1200

• 12x + 400 > 1200

• 12x + 400 < 1200

Your taxi fare is $2.50 per mile, plus a $5 fee.  You cannot exceed $20.  Which inequality models this scenario?

• 5x + 2.50 ≤ 20

• 2.50x + 5 < 20

• 2.50x + 5 ≤ 20

• 7.50x < 20

What are the correct steps to solving this inequality?

• Subtract 12, then divide by 3, then reverse the inequality sign.

• Add 12, then multiply by -3, then reverse the inequality sign.

• Add 12, then divide by -3, then reverse the inequality sign.

• Subtract 12, then divide by -3, then reverse the inequality sign.

Which operations must we UNDO to solve this inequality?

• Subtraction, then multiplication

• Multiplication, then division

• Addition, then division.

• Addition, then subtraction

What is the first step to solving this inequality?

• Add 9 to both sides of the inequality.

• Divide both sides of the inequality by 9.

• Subtract 6 on both sides of the inequality.

• Add 6 to both sides of the inequality.

What is the first step to solve the following inequality?

• Multiply both sides of the inequality by -6

• Subtract 17 on both sides of the inequality.

• Divide both sides of the inequality by -6

• Add 17 to both sides of the inequality.

What is the first step to solve the following inequality?

• Subtract 25 from both sides of the inequality.

• Add 25 to both sides of the inequality.

• Divide both sides of the inequality by 4.

• Multiply both sides of the inequality by -4.

9 ≥ -2m + 2 − 3

• m ≤ 5

• m ≤ -5

• m ≥ -5

• m ≥ 5

• n < 1
• n < -1
• n > 1
• n > -1