Question

1. simplify the following expression 23 - 6(8 - 3)
2. combine like terms - x + 2x + 3x² - 4x - 18x² + 5x - 6
3. combine like terms - 2x + 3x² + 4x - 2x²
4. solve the following equation - 6 + p = 14
5. circle the property that justifies line 1 to line 2 line 1: (2x + 3x) + 4x line 2: 2x + (3x + 4x) commutative, associative, or distributive
6. circle the property that justifies line 1 to line 2 line 1: (ab)c line 2: a(bc) commutative, associative, or distributive
7. based on the number line, find the inequality?
8. based on the inequality, draw the number line. x ≤ 2

Explanation:

Step1: Simplify the expression in 1)

First, calculate the value inside the parentheses: $8 - 3=5$. Then, multiply: $6\times5 = 30$. Finally, subtract: $23-30=-7$.

Step2: Combine like - terms in 2)

Combine the $x^2$ terms: $3x^2-18x^2=-15x^2$. Combine the $x$ terms: $-x + 2x-4x + 5x=2x$. So the simplified expression is $-15x^2+2x - 6$.

Step3: Combine like - terms in 3)

Combine the $x^2$ terms: $3x^2-2x^2=x^2$. Combine the $x$ terms: $-2x + 4x = 2x$. So the simplified expression is $x^2+2x$.

Step4: Solve the equation in 4)

Add 6 to both sides of the equation $-6 + p=14$. We get $p=14 + 6=20$.

Step5: Identify the property in 5)

The change from $(2x + 3x)+4x$ to $2x+(3x + 4x)$ is an example of the associative property of addition.

Step6: Identify the property in 6)

The change from $(ab)c$ to $a(bc)$ is an example of the associative property of multiplication.

Step7: Find the inequality in 7)

The open - circle at 6 and the arrow pointing to the left represents the inequality $x<6$.

Step8: Draw the number line in 8)

Draw a number line. Mark a closed - circle at 2 (since the inequality is $x\leq2$) and draw an arrow pointing to the left.

Answer:

1. $-7$
2. $-15x^2+2x - 6$
3. $x^2+2x$
4. $p = 20$
5. Associative
6. Associative
7. $x<6$
8. Draw a number line with a closed - circle at 2 and an arrow pointing left.