Solve the following equation for x. ³⁄₅x - 3 = 9

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When solving an equation with one variable, your goal is to isolate the variable on one side of the equal sign. You do this by moving all of the other numbers to the opposite of the equal sign. You move numbers by performing the opposite operation (subtraction/addition and multiplication/division), on both sides of the equation to keep it balanced. For this problem: Step 1: Begin to isolate variable by moving numbers that are being added or subtracted to the other side of the equation. Note: We want to move numbers NOT attached to a variable first, if possible. The first thing you want to do is move the ( - 3) to the other side of the equation by adding 3 (opposite operation) to both sides. ³⁄₅x - 3 + 3 = 9 + 3 ³⁄₅x = 12 Step 2: Continue to isolate variable by moving numbers that are being multiplied or divided to the other side of the equation. Then, you need to move the ³⁄₅, which is multiplying x. You do this by dividing (opposite operation) both sides by ³⁄₅. *Remember that when you divide by a fraction, you multiply by its reciprocal, which in this case is ⁵/₃. ⁵/₃• ³⁄₅x = 12 • ⁵/₃ When you multiply two fractions, you can cross-reduce before you multiply across: 11ec0fb7_2739_21f9_95f0_c3973e745aef_NR0002_00 Reduce the numbers diagonal from one another by finding the lowest common factor between the two numbers, then dividing each number by the lowest common factor. The lowest common factor for 12 and 3 is 3. You can reduce both 3's by dividing by 3. This results in each 3 being reduced to 1. You can also reduce both 5's by dividing by 5. This results in each 5 being reduced to 1. 11ec0fb7_2739_21fa_95f0_e3d61bf28ae4_NR0002_00 Now, your new fraction is: 11ec0fb7_2739_21fb_95f0_9f8f4aebf4b0_NR0002_00 We know that this comes out equal to 1, so now we have 1x, which is the same as just x. Step 3: Complete the remaining operations on the opposite side of the equation. x = 12 • ⁵/₃ Since 12 is a whole number, we make it a fraction by making 12 the numerator and 1 the denominator. Reduce the numbers diagonal from one another by finding the lowest common factor between the two numbers, then dividing each number by the lowest common factor. 11ec0fb7_2739_21fc_95f0_4952650bbabd_NR0002_00 In this case, the lowest common factor between 12 and 3 is 3, so we divide both numbers by 3. 5 and 1 do not have any common multiples other than 1, so these numbers cannot be reduced. 11ec0fb7_2739_490d_95f0_af5f7371f10d_NR0002_00 Finally, we multiple the two numerators and two denominators together to reach the final answer. 11ec0fb7_2739_490e_95f0_59717d60aa51_NR0002_00 Answer: 20

Solve the Following Equation for X