Algebra Review an example | All parts she

Sure! Let's go through an example of an algebra problem step by step. We'll cover various parts of algebra, including solving equations, working with inequalities, and simplifying expressions. ### Example Problem: Solve the Equation **Problem:** Solve the equation \( 2x + 3 = 11 \). #### Step 1: Isolate the variable To solve for \( x \), we want to isolate it on one side of the equation. We can start by subtracting 3 from both sides: \[ 2x + 3 - 3 = 11 - 3 \] This simplifies to: \[ 2x = 8 \] #### Step 2: Solve for \( x \) Next, we divide both sides by 2 to solve for \( x \): \[ \frac{2x}{2} = \frac{8}{2} \] This gives us: \[ x = 4 \] ### Example Problem: Solve the Inequality **Problem:** Solve the inequality \( 3x - 5 < 7 \). #### Step 1: Isolate the variable First, we add 5 to both sides: \[ 3x - 5 + 5 < 7 + 5 \] This simplifies to: \[ 3x < 12 \] #### Step 2: Solve for \( x \) Next, we divide both sides by 3: \[ \frac{3x}{3} < \frac{12}{3} \] This gives us: \[ x < 4 \] ### Example Problem: Simplifying an Expression **Problem:** Simplify the expression \( 4(2x + 3) - 2(x - 1) \). #### Step 1: Distribute First, we distribute the 4 and the -2: \[ 4(2x) + 4(3) - 2(x) + 2(1) \] This simplifies to: \[ 8x + 12 - 2x + 2 \] #### Step 2: Combine like terms Now, we combine the like terms: \[ (8x - 2x) + (12 + 2) \] This gives us: \[ 6x + 14 \] ### Summary - We solved the equation \( 2x + 3 = 11 \) and found \( x = 4 \). - We solved the inequality \( 3x - 5 < 7 \) and found \( x < 4 \). - We simplified the expression \( 4(2x + 3) - 2(x - 1) \) to get \( 6x + 14 \). If you have any specific topics or problems in algebra that you would like to review, feel free to ask!