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Solving Two-Step Equations and Finding Function Inputs

This guide focuses on solving two-step equations by combining like terms and finding inputs of functions. Learn to solve equations such as (7x - 4x = 21) and understand how to derive function outputs, like when the output is 3 less than 5 times the input. Each example walks you through simplifying and checking your solutions. With practice problems included, you can reinforce your understanding and master similar mathematical challenges in function evaluation and linear equations.

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Solving Two-Step Equations and Finding Function Inputs

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  1. = 3x 21 3 3 EXAMPLE 2 Solve a two-step equation by combining like terms Solve7x – 4x = 21 7x – 4x = 21 Write original equation. 3x = 21 Combine like terms. Divide each side by 3. x = 7 Simplify.

  2. SOLUTION STEP1 Write an equation for the function. Let xbe the input and ybe the output STEP 2 Solve the equation for xwhen y =17. EXAMPLE 3 Find an input of a function The output of a function is 3 less than 5 times the input. Find the input when the output is 17. y = 5x – 3 yis 3 less than 5 times x.

  3. 20 5x = 5 5 ANSWER An input of4 produces an output of17. EXAMPLE 3 Find an input of a function y = 5x – 3 Write original function. 17 = 5x – 3 Substitute17 fory. 17 + 3= 5x – 3 +3 Add 3 to each side. 20 = 5x Simplify. Divide each side by5. 4 = x Simplify.

  4. ? 17 = 5(4) – 3 ? 17 = 20– 3 17 = 17 EXAMPLE 3 Find an input of a function CHECK y = 5x– 3 Write original function. Substitute 17 for yand 4 for x. Multiply 5 and 4. Simplify. Solution checks.

  5. ANSWER 4 for Examples 2 and 3 GUIDED PRACTICE Solve the equation. Check your solution. 4. 4w + 2w = 24

  6. ANSWER 7 for Examples 2 and 3 GUIDED PRACTICE Solve the equation. Check your solution. 5. 8t – 3t = 35

  7. ANSWER 4 for Examples 2 and 3 GUIDED PRACTICE Solve the equation. Check your solution. 6. –16= 5d – 9d

  8. 7. The output of a function is 5 more than –2 times the input. Find the input when the output is 11. ANSWER –3 for Examples 2 and 3 GUIDED PRACTICE

  9. 8. The output of a function is 4 less than 4 times the input. Find the input when the output is 3 3 ANSWER 1 4 for Examples 2 And 3 GUIDED PRACTICE

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