Solve x – 5y = 6 for x.
The Correct Answer and Explanation is:
Correct Answer:
To solve the equationx−5y=6x – 5y = 6 x−5y=6
for x, we need to isolate x on one side of the equation.
Start by adding 5y to both sides:x=6+5yx = 6 + 5y x=6+5y
This is the required solution. The equation solved for x is:x=6+5yx = 6 + 5y x=6+5y
Explanation:
This equation is a linear equation in two variables: x and y. When asked to solve for x, the goal is to express x in terms of y. This involves isolating x on one side of the equation so that it stands alone.
The original equation is:x−5y=6x – 5y = 6x−5y=6
In this form, x is being subtracted by 5y. To undo this subtraction, we do the opposite — we add 5y to both sides of the equation. This keeps the equation balanced, meaning both sides remain equal. When we perform the operation, it looks like this:x−5y+5y=6+5yx – 5y + 5y = 6 + 5yx−5y+5y=6+5y
On the left side, -5y + 5y cancels out, leaving only x. The right side becomes 6 + 5y. The result is:x=6+5yx = 6 + 5yx=6+5y
This new equation expresses x entirely in terms of y, which means we have successfully solved the equation for x.
This result can be helpful in algebra when graphing or substituting into another equation. For example, if you are given a value of y, you can quickly find x using this new equation. If y = 2, then:x=6+5(2)=6+10=16x = 6 + 5(2) = 6 + 10 = 16x=6+5(2)=6+10=16
This shows how solving for one variable gives a formula that makes further calculations much easier.
