lesson menu main idea example 1:solve multi-step inequalities example 2:solve multi-step...
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Main Idea
Example 1: Solve Multi-Step Inequalities
Example 2: Solve Multi-Step Inequalities
• Use properties of inequality to solve multi-step inequalities.
Solve Multi-Step Inequalities
Solve –4d + 2(d + 5) > 12. Graph the solution set on a number line.
–4d + 2(d + 5) > 12 Write the equation.–4d + 2d + 10 > 12 Distributive Property
–2d + 10 > 12 Simplify.– 10 > – 10 Subtraction Property of Inequality
–2d > 2 Simplify.
d < –1 Simplify.
Division Property of Inequality;reverse inequality symbol.
Graph the solution set on a number line. Use an open dot because –1 is not included.
Solve Multi-Step Inequalities
Answer: d < –1;
Solve 3(n – 1) + 5n 5. Graph the solution set on a number line.
A. n ≥ –1;
B. n ≥ ;
C. n < 1;
D. n ≤ 1;
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PAINT Rami can spend $550 at most to have 3 rooms painted. A painter charges d dollars per room to paint and $35 per room for prep work. There is a one-time $70 charge for supplies. Write and solve an inequality to find the maximum Rami can spend for painting a room.
Solve Multi-Step Inequalities
Solve Multi-Step Inequalities
3(d + 35) + 70 ≤ 550 Write the equation.3d + 105 + 70 ≤ 550 Distributive Property
3d + 175 ≤ 550 Simplify.– 175 – 175 Subtraction Property of Inequality
3d ≤ 375 Simplify.
d ≤ 125 Simplify.
Division Property of Inequality
Answer: So, the maximum Rami can spend for painting a room is $125.
A. 4(12 + d) ≤ 80; d ≤ $8.00
B. 4(7 + d) + 5 ≤ 80; d ≤ $11.75
C. 4(5 + d) + 7 ≤ 80; d ≤ $13.25
D. 4d + 7 + 5 ≤ 80; d ≤ $17.00
FAIR A family of four can spend $80 at most at the fair. Parking costs $5 and each ticket costs $7. Each person is given d dollars to spend on food and drinks. Write and solve an inequality to find the maximum amount each person can spend on food and drinks.