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Solving Equations and Verbal Modeling with Examples

This text provides examples and solutions for solving equations, including verbal modeling, in a step-by-step manner. It covers different types of equations and includes helpful tips for checking solutions.

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Solving Equations and Verbal Modeling with Examples

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  1. Solve x + 8 = 20. x + 8 = 20 x = (12) x = 12 4 5 Multiply each side by , the reciprocal of . 4 5 The solution is 15. ANSWER CHECK x = 15 in the original equation. 4 4 4 4 5 4 5 4 5 5 5 5 (15) + 8 = 12 + 8 = 20 x+ 8 = EXAMPLE 1 Solve an equation with a variable on one side Write original equation. Subtract 8 from each side. x = 15 Simplify.

  2. Restaurant During one shift, a waiter earns wages of $30 and gets an additional 15% in tips on customers’ food bills. The waiter earns $105. What is the total of the customers’ food bills? Write a verbal model. Then write an equation. Write 15% as a decimal. EXAMPLE 2 Write and use a linear equation SOLUTION

  3. ANSWER The total of the customers’ food bills is $500. EXAMPLE 2 Write and use a linear equation 105 = 30 + 0.15x Write equation. 75 = 0.15x Subtract 30 from each side. 500 = x Divide each side by 0.15.

  4. 3. – x + 1 = 4 The solution is x = 3. The solution is x = 4. The solution is 5. ANSWER ANSWER ANSWER 3 5 for Examples 1 and 2 GUIDED PRACTICE Solve the equation. Check your solution. 1. 4x + 9 = 21 2. 7x – 41 = – 13

  5. ANSWER The agent must sell $950,000 in a year to each $ 60000 for Examples 1 and 2 GUIDED PRACTICE 4. REAL ESTATE A real estate agent’s base salary is $22,000 per year. The agent earns a 4% commission on total sales. How much must the agent sell to earn $60,000 in one year?

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