Welcome to an example on how to solve an linearequation and one variable.
It's important to remember,when solving equations, in each step in the solution process, we are acquitting an equivalent equation and, therefore, whateveroperation we perform on one side of the equation, we must also perform on the other.
Looking at the notes below, in general, the first step insolving a linear equation is to simplify each side of the equation by clearing parenthesesand combining like terms.
But, for the given equation, we cannot simplify the left or right side, and, therefore, we move to the next step, which is to add or subtract to isolate the variable term on oneside of the equation.
Notice right now, the variableterm is on the left side, and the variable term is negative three x, which means the first step isto isolate negative three x on the left side of the equation.
Which means we need toundo this positive 15.
To undo positive 15, againby adding or subtracting, we need to subtract 15.
The first step is to subtract 15 on both sides of the equation.
Again, we subtract 15 on both sides, so the result is an equivalent equation.
Now we simplify.
15 minus 15 is zero.
The left side simplifiesto negative three x equals on the right side,36 minus 15 is equal to 21.
So the equation negative three x equals 21 is equivalent to the given equation, except now the variable term is isolated.
The next step is to multiply or divide to isolate the variableterm and solve the equation.
We need to be careful herebecause the negative three and the x are attached by multiplication.
Negative three x meansnegative three times x.
And, therefore, to undo the multiplication and solve for x, we need to divide both sides of the equationby negative three.
And now we simplify.
Negative three divided bynegative three is equal to one.
One times x is x.
We have x equals 21divided by negative three is equal to negative seven.
And, once again, this is an equivalent equation to the given equation, except now the equation is solved for x, and, therefore, it gives usthe solution to the equation.
Our solution is x equals negative seven, which means if we substitutenegative seven for x into the equation, itmust satisfy the equation, meaning the expression onthe left side of the equation and the right side must havethe same value or equal value.
And that's why the last step is always to check the solution.
So, let's go ahead and check our solution by substituting negative seven for x, which give us 15 minus three times negative seven equals 36.
And now we simplify theleft side of the equation.
Simplifying here, we have minusthree times negative seven, which is minus negative 21,which is equivalent to plus 21.
The left side simplifiesto 15 plus 21 equals 36.
15 plus 21 is 36.
36 equals 36 is true, verifyingour solution is correct.
I hope you found this helpful.