Solving Multi-Step Equations and Inequalities

This video tutorial by Mr. Richards covers solving multi-step equations and inequalities, including distribution, identities, and equations with no solutions. It also explores solving and checking multi-step inequalities and applying them to real-world scenarios. The lesson concludes with graphing solutions on a number line.

What is the first step in solving the equation 6(B - 2) = 2(2B + 8)?

• Add 12 to both sides

• Distribute the constants

• Combine like terms

• Subtract 2B from both sides

After distributing in the equation 6(B - 2) = 2(2B + 8), what is the next step?

• Combine like terms

• Add 12 to both sides

• Divide by 2

• Subtract 4B from both sides

What is the solution to the equation 6(B - 2) = 2(2B + 8)?

• B = 12

• B = 14

• B = 18

• B = 16

What does it mean if an equation simplifies to 9 = 9?

• The equation has no solution

• The equation is an identity

• The equation has one solution

• The equation is inconsistent

What is the result when solving the equation 7y - 8 = 3(2y + 4) + y?

• y = -2

• y = 2

• All real numbers

• No solution

What is the first step in solving the inequality 2(X - 5) ≤ 1?

• Distribute the 2

• Divide by 2

• Subtract 2 from both sides

• Add 5 to both sides

What is the solution to the inequality 2(X - 5) ≤ 1?

• X ≤ 3

• X ≤ 4

• X ≤ 5

• X ≤ 5.5

How much can the company spend per guest on food if the total budget is $1825, the facility costs $225, and there is a $3 charge per guest for linens with 80 guests?

• $15

• $18

• $16

• $17

What is the first step in solving the inequality 5X - 9 ≥ 2X + 6?

• Distribute the 2

• Divide by 5

• Add 9 to both sides

• Subtract 2X from both sides

When graphing the solution to the inequality X ≥ 7, what should you do?

• Shade to the right of 7

• Shade both sides of 7

• Shade to the left of 7

• Do not shade at all