By Barbara Jund
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Extra resources for Algebra success in 20 minutes a day
According to the order of operations that you learned in the previous lesson, you would have to do the grouping symbols first. However, you know you can’t add x to y because they are not like terms. What you need to do is use the distributive property. The distributive property tells you to multiply the number and/or variable(s) outside the parentheses by every term inside the parentheses. You would work the problem like this: 28 Team-LRN – COMBINING LIKE TERMS – Multiply 2 times x and 2 times y.
Subtract 15 from both sides of the equation. Simplify both sides of the equation. Subtract 3x from both sides of the equation. Simplify both sides of the equation. Your common sense tells you that 0 will never equal 15. This means there is no value of the variable that will make the equation true because 0 will never equal 15. Since there is no value of x that will ever make the equation true, there is no solution. When there is no solution, it is called an empty set. This notation л is used for the empty set.
4x – 3 + 3x = –2x + 5 – 17 ______26. 9x – (x + 3) = 2(x + 4) + 7 ______22. 12x + 2 – 5x = 3(x + 5) + 3 ______27. 5(2x + 3) = 4(x – 1) + 1 ______23. 12x – 11x + 5 = –2(x + 3) + 5 ______28. 8 – 4x ______24. 5 – (x – 3) = 10 – 3x ______29. 13x – 2(3x – 4) = 6(x + 2) – 4 ______25. 3x + 2 – 6x = 8 + 3(x + 2) ______30. 13x – 3(–2x – 3) = 4(x + 4) – 12 Equations Without a Variable in the Answer In some equations, all the variables will be eliminated. These are special cases, and the equations may or may not have solutions.
Algebra success in 20 minutes a day by Barbara Jund