Questions: Simplifying Expressions Simplify the expressions completely. 5-(x+8) 5-2(4x+9) 8(x+5)+3x

Transcript text: Simplifying Expressions Simplify the expressions completely. \[ \begin{array}{l} 5-(x+8) \\ 5-2(4 x+9) \\ 8(x+5)+3 x \end{array} \] Question Help: Video Message instructor

Solution

Solution Steps

To simplify the given expressions, we will apply the distributive property and combine like terms. For each expression, distribute any coefficients and then combine any terms that are similar.

Step 1: Simplify the First Expression

The first expression is \(5 - (x + 8)\). To simplify, distribute the negative sign across the terms inside the parentheses: \[ 5 - (x + 8) = 5 - x - 8 \] Combine like terms: \[ 5 - 8 - x = -x - 3 \]

Step 2: Simplify the Second Expression

The second expression is \(5 - 2(4x + 9)\). First, distribute the \(-2\) across the terms inside the parentheses: \[ 5 - 2(4x + 9) = 5 - 8x - 18 \] Combine like terms: \[ 5 - 18 - 8x = -8x - 13 \]

Step 3: Simplify the Third Expression

The third expression is \(8(x + 5) + 3x\). Distribute the \(8\) across the terms inside the parentheses: \[ 8(x + 5) + 3x = 8x + 40 + 3x \] Combine like terms: \[ 8x + 3x + 40 = 11x + 40 \]