To solve the problem of simplifying the given linear expressions, we will follow these steps:
1.
Distribute any coefficients or negative signs inside parentheses.
2.
Combine like terms (terms with the same variable and constant terms).
3.
Write the simplified expression in standard form.
Let's go through each expression step by step.
---
Expression 1: $-5(4x + 7)$
1. Distribute $-5$ to both terms inside the parentheses:
\[
-5(4x) + (-5)(7) = -20x - 35
\]
2. There are no like terms to combine.
3. The simplified expression is:
\[
\boxed{-20x - 35}
\]
---
Expression 2: $-3(-5x - 8)$
1. Distribute $-3$ to both terms inside the parentheses:
\[
-3(-5x) + (-3)(-8) = 15x + 24
\]
2. There are no like terms to combine.
3. The simplified expression is:
\[
\boxed{15x + 24}
\]
---
Expression 3: $-(2x - 9)$
1. Distribute the negative sign to both terms inside the parentheses:
\[
-(2x) + (-1)(-9) = -2x + 9
\]
2. There are no like terms to combine.
3. The simplified expression is:
\[
\boxed{-2x + 9}
\]
---
Expression 4: $-(-3x + 11)$
1. Distribute the negative sign to both terms inside the parentheses:
\[
-(-3x) + (-1)(11) = 3x - 11
\]
2. There are no like terms to combine.
3. The simplified expression is:
\[
\boxed{3x - 11}
\]
---
Expression 5: $-2(3x - 4)$
1. Distribute $-2$ to both terms inside the parentheses:
\[
-2(3x) + (-2)(-4) = -6x + 8
\]
2. There are no like terms to combine.
3. The simplified expression is:
\[
\boxed{-6x + 8}
\]
---
Expression 6: $-(-4x + 17)$
1. Distribute the negative sign to both terms inside the parentheses:
\[
-(-4x) + (-1)(17) = 4x - 17
\]
2. There are no like terms to combine.
3. The simplified expression is:
\[
\boxed{4x - 17}
\]
---
Expression 7: $-(3x - 12)$
1. Distribute the negative sign to both terms inside the parentheses:
\[
-(3x) + (-1)(-12) = -3x + 12
\]
2. There are no like terms to combine.
3. The simplified expression is:
\[
\boxed{-3x + 12}
\]
---
Final Answer:
\[
\boxed{
\begin{aligned}
1. & \quad -20x - 35 \\
2. & \quad 15x + 24 \\
3. & \quad -2x + 9 \\
4. & \quad 3x - 11 \\
5. & \quad -6x + 8 \\
6. & \quad 4x - 17 \\
7. & \quad -3x + 12
\end{aligned}
}
\]
Parent Tip: Review the logic above to help your child master the concept of simplifying algebraic expressions worksheet with answers.
