Linear Equations

How to solve linear equations

Steps to Solve Linear Equations

5x - 8 + 2x - 2 = 7x - 1 - 3x - 3 The first step you should do is to simplify both sides of the equation by collecting the common terms containing variable x and the common constant terms separately at each side of the equation. Let us do it. By collecting common terms with the variable x at the left side, you will get 5x + 2x = 7x. By collecting common constant terms at the left side you will get -8 - 2 = -10. Thus, now the left side is 7x - 10. Making similar calculations at the right side of the equation, you will get the right side 4x - 4. After these simplifications your equation has the form 7x - 10 = 4x - 4. The first step is done. The second step is to collect terms containing variable x in one side of the equation and make the other side of the equation free of variable terms. Let us do it. Subtract 4x from both sides. You will have 7x - 4x -10 = 4x - 4x - 4. Collect common terms. You will have 3x - 10 = -4. Very good, now the term with the variable x, which is 3x in this case, is in the left side and there are no terms with the x at the right side. The second step is done. The third step is to collect all the constant terms in the right side and make the left side free of constants. Let us do it. Add 10 to both sides. You will have 3x - 10 + 10 = -4 + 10. Collect common terms. You will have 3x = 6. The third step is done. Your equation is very simple now: it contains only one variable term at the left side and only one constant term at the right side. The fourth step is to divide both sides of your equation by the coefficient at x. You will get an expression of the form x = the value, which is going to be a solution. Let us do it. Divide both side of the last equation by 3. When you divide, you will get x = 2. The fourth step is done. The value of 2 is going to be the solution of your equation. The last step in solving the equation is to check the solution. In order to do it, simply substitute the found value of the variable x into the original equation, then calculate and compare both sides. Let us do it. Substitute the found solution x = 2 into the original equation. The left side is 5*2 - 8 + 2*2 - 2 = 10 - 8 + 4 - 2 = 4. The right side is 7*2 - 1 - 3*2 - 3 = 14 - 1 -6 -3 = 4. So, we conclude that the found solution x = 2 is correct. Answer: the solution is x = 2.