Let's solve each of your questions step by step.
Inequality 1:
Solve the inequality: \[ -(3x+3) - 2x > -4(x-2) - 2 \]
Step 1: Distribute on both sides: Distributing gives us: \[ -3x - 3 - 2x > -4x + 8 - 2 \]
Step 2: Combine Like Terms: Combine like terms on both sides: \[ -5x - 3 > -4x + 6 \]
What is the second step in solving the inequality?
In this case, the second step is combining like terms after distributing. The appropriate option is:
- Combine Like Terms
Inequality 2:
Solve the inequality: \[ 5x - 3(x + 6) \geq 8 - (x - 7) \]
Step 1: Distribute on both sides: \[ 5x - 3x - 18 \geq 8 - x + 7 \]
Step 2: Combine Like Terms: On the left side: \[ 2x - 18 \geq 15 - x \]
Step 3: Add x to both sides: \[ 2x + x - 18 \geq 15 \]
Step 4: Combine Like Terms again: \[ 3x - 18 \geq 15 \]
Step 5: Add 18 to both sides:
\[ 3x \geq 33 \]
Step 6: Divide by 3:
\[ x \geq 11 \]
Solve for y in terms of x:
Given \( y < mx + b \): To express \( y \) in terms of \( x \): \[ y < mx + b \] This is already solved for \( y \).
Given \( ax + by \leq c \): To solve for \( y \):
- Move \( ax \) to the right side: \[ by \leq c - ax \]
- Divide by \( b \) (assuming \( b \neq 0 \)): \[ y \leq \frac{c - ax}{b} \]
If \( b \) is negative, you must reverse the inequality sign: \[ y \geq \frac{c - ax}{b} \]
Final Summary:
- The second step in the first inequality is Combine Like Terms.
- The inequality \( x \geq 11 \) is the solution for the second inequality.
- \( y \) is solved from \( y < mx + b \) and rearranged from \( ax + by \leq c \) to \( y \leq \frac{c - ax}{b} \).
1 answer