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AF1.1 Write and solve one-step linear equations in one variable.

California Standards. AF1.1 Write and solve one-step linear equations in one variable. Multiplying by a number is the inverse of dividing by that number. When an equation contains division, use multiplication to “undo” the division. 35. x. x. x. = 5. = 5. = 5. = 5. 7.

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AF1.1 Write and solve one-step linear equations in one variable.

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  1. California Standards AF1.1 Write and solve one-step linear equations in one variable.

  2. Multiplying by a number is the inverse of dividing by that number. When an equation contains division, use multiplication to “undo” the division.

  3. 35 x x x = 5 = 5 = 5 = 5 7 7 7 7 x is divided by 7. x 7 = 7 5 7 Check ? ? 5 = 5 Example 1A: Solving Equations by Multiplying Solve the equation. Check your answer. Multiply both sides by 7 to undo the division. x = 35 Substitute 35 forx in the equation. 35 is the solution. 

  4. 78 p p p 13 = 13 = 13 = 13 = 6 6 6 6 p is divided by 6. p 6 13 = 6 6 Check ? ? 13 = 13 Additional Example 1B: Solving Equations by Multiplying Solve the equation. Check your answer. Multiply both sides by 6 to undo the division. 78= p Substitute 78 forp in the equation.  78 is the solution.

  5. h 3 14 = 3 3 h Substitute 14 for height of aspen. h is divided by 3. 14 = 3 Example 2: Application At Elk Meadows Park an aspen tree is one-third the height of a pine tree. height of pine height of aspen = 3 The aspen tree is 14 feet tall. How tall is the pine tree? Let h represent the height of the pine tree. Multiply both sides by 3 to undo the division. 42= h The pine tree is 42 feet tall.

  6. p p p 72 = 72 = 72 = 4 4 4 p is divided by 4. p 4 72 = 4 4 Check 288 ? 72 = 4 ? 72 = 72 Check It Out! Example 1 Solve the equation. Check your answer. Multiply both sides by 4 to undo the division. 288 = p Substitute 288 forp in the equation. 288 is the solution. 

  7. w 95 = 2 Substitute 95 for Jamie’s weight. w is divided by 2. w 2 2 95 = 2 Check It Out! Example 2 Jamie weighs one-half as much as her father. father’s weight Jamie’s weight = 2 Jamie weighs 95 pounds. How many pounds does her father weigh? Let w represent her father’s weight. Multiply both sides by 2 to undo the division. 190 = w Jamie’s father weighs 190 pounds.

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