Holt McDougal Algebra Solving Equations with Variables on Both Sides Algebra 1 Review

Holt McDougal Algebra Solving Equations with Variables on Both Sides Quiz 1. Squares from 1 to 12? 2. What is i? 3. Define slope? 4. What is a coordinate?

Holt McDougal Algebra Solving Equations with Variables on Both Sides To solve an equation with variables on both sides, use inverse operations to "collect" variable terms on one side of the equation.

Holt McDougal Algebra Solving Equations with Variables on Both Sides Solve 7n – 2 = 5n + 6. Example 1: Solving Equations with Variables on Both Sides To collect the variable terms on one side, subtract 5n from both sides. 7n – 2 = 5n + 6 –5n 2n – 2 = 6 Since n is multiplied by 2, divide both sides by 2 to undo the multiplication. 2n = n = 4

Holt McDougal Algebra Solving Equations with Variables on Both Sides Solve 4b + 2 = 3b. Check It Out! Example 1a To collect the variable terms on one side, subtract 3b from both sides. 4b + 2 = 3b –3b b + 2 = 0 b = –2 – 2 – 2

Holt McDougal Algebra Solving Equations with Variables on Both Sides Solve y = 0.7y – 0.3. Check It Out! Example 1b To collect the variable terms on one side, subtract 0.3y from both sides y = 0.7y – 0.3 –0.3y 0.5 = 0.4y – = 0.4y = y Since 0.3 is subtracted from 0.4y, add 0.3 to both sides to undo the subtraction. Since y is multiplied by 0.4, divide both sides by 0.4 to undo the multiplication.

Holt McDougal Algebra Solving Equations with Variables on Both Sides Distribution Property 5(x + 7) 5(x) + 5(7) 5x + 35

Holt McDougal Algebra Solving Equations with Variables on Both Sides Solve 4 – 6a + 4a = –1 – 5(7 – 2a). Example 2: Simplifying Each Side Before Solving Equations Combine like terms. Distribute –5 to the expression in parentheses. 4 – 6a + 4a = –1 –5(7 – 2a) 4 – 6a + 4a = –1 –5(7) –5(–2a) 4 – 6a + 4a = –1 – a 4 – 2a = – a – 2a = 10a + 2a +2a 40 = 12a Since –36 is added to 10a, add 36 to both sides. To collect the variable terms on one side, add 2a to both sides.

Holt McDougal Algebra Solving Equations with Variables on Both Sides Solve 4 – 6a + 4a = –1 – 5(7 – 2a). Example 2 Continued 40 = 12a Since a is multiplied by 12, divide both sides by 12.

Holt McDougal Algebra Solving Equations with Variables on Both Sides Solve. Check It Out! Example 2a Since 1 is subtracted from b, add 1 to both sides. Distribute to the expression in parentheses = b – 1 To collect the variable terms on one side, subtract b from both sides = b

Holt McDougal Algebra Solving Equations with Variables on Both Sides Solve 3x + 15 – 9 = 2(x + 2). Check It Out! Example 2b Combine like terms. Distribute 2 to the expression in parentheses. 3x + 15 – 9 = 2(x + 2) 3x + 15 – 9 = 2(x) + 2(2) 3x + 15 – 9 = 2x + 4 3x + 6 = 2x + 4 –2x x + 6 = 4 – 6 – 6 x = –2 To collect the variable terms on one side, subtract 2x from both sides. Since 6 is added to x, subtract 6 from both sides to undo the addition.

Holt McDougal Algebra The Slope Formula Example 1: Finding Slope by Using the Slope Formula Find the slope of the line that contains (2, 5) and (8, 1). Use the slope formula. Substitute (2, 5) for (x 1, y 1 ) and (8, 1) for (x 2, y 2 ). Simplify. The slope of the line that contains (2, 5) and (8, 1) is.

Holt McDougal Algebra Slope-Intercept Form Additional Example 1: Graphing by Using Slope and y-intercept Graph the line given the slope and y-intercept. Step 1 The y-intercept is 4, so the line contains (0, 4). Plot (0, 4). Step 3 Draw the line through the two points. Run = 5 Rise = –2 Step 2 Slope = Count 2 units down and 5 units right from (0, 4) and plot another point. y ; y intercept = 4 Slope =-