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9.3

Further Solving Linear Equations. 9.3. To Solve Linear Equations in One Variable. Solving linear equations in one variable Step 1: If an equation contains fractions, multiply both sides by the LCD to clear the equation of fractions.

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9.3

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  1. Further Solving Linear Equations 9.3

  2. To Solve Linear Equations in One Variable Solving linear equations in one variable Step 1: If an equation contains fractions, multiply both sides by the LCD to clear the equation of fractions. Step 2: Use the distributive property to remove parentheses if they are present. Step 3: Simplify each side of the equation by combining like terms. Continued

  3. To Solve Linear Equations in One Variable Step 4: Get all variable terms on one side and all numbers on the other side by using the addition property of equality. Step 5: Get the variable alone by using the multiplication property of equality. Step 6: Check the solution by substituting it into the original equation.

  4. Multiply both sides by 5. Simplify. Add –3y to both sides. Add –30 to both sides. Divide both sides by 7. Simplify. Solving Linear Equations Example Solve:

  5. Solving Linear Equations Example Solve: 5x – 5 = 2(x + 1) + 3x – 7 5x – 5 = 2(x + 1) + 3x – 7 5x – 5 = 2x + 2 + 3x – 7 Apply the distributive property. 5x – 5 = 5x – 5 Combine like terms. Both sides of the equation are identical. Since this equation will be true for every x that is substituted into the equation, the solution is “all real numbers.”

  6. 3x + (– 3x) – 7 = 3x + (– 3x) + 3 Add –3x to both sides. Solving Linear Equations Example Solve: 3x – 7 = 3(x + 1) 3x – 7 = 3(x + 1) 3x – 7 = 3x + 3 Apply the distributive property. – 7 = 3 Simplify. Since no value for the variable x can be substituted into this equation that will make this a true statement, there is “no solution.”

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