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Solve for the specified variable or expression.$$\frac{7}{8} c+w=9 \text { for } c$$
$$c=\frac{72-8 w}{7}$$
Precalculus
Algebra
Chapter 2
Equations, Inequalities, and Problem Solving
Section 4
Formulas
Algebra Topics That are Reviewed at the Start of the Semester
Equations and Inequalities
Missouri State University
Baylor University
Lectures
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forgiven the equation. Seven h c plus w is equal to night on we're trying to solve for C. In other words, we need to isolate see on either side of our equation. Well, the first thing I noticed is that we have a fraction. I typically like to get rid of fractions first and equations, while in this fraction we have that seven is getting divided by eight Soto. Undo it. I'm going to multiply both sides of my equation by eight. Now, on the left hand side, that means I need to distribute to eight to both of those terms well, eight times. Seven h c well, eight times 7/8 would be 56 8th but 56 divided by eight is just seven, so we're just left with seven C. Next, I need to pull two ply eight times W well, eight times w is just eight w Now on the right hand side, I have nine times eight, which is 72. Keep in mind we want to get C by itself. Well, we're adding eight w to the term seven c. Well, I need to move that eight w to the other side. Well, what's the opposite of adding eight W? Well, that would be subtracted eight of you. So I'm going to subtract eight w from both sides of the equation. So the seven C will just come down well, eight w minus eight w zero. So those terms cancel. And on the right hand side of the equation, you have 72 minus eight W Well, those air not like terms and therefore cannot be combined. So we will be loved with 72 minus eight w Lastly, see is now getting times by seven. Well, what's the opposite? Well, that would be to divide by seven. So I'm gonna divide both sides. My equation by seven. Now, on the left hand side seven, divided by seven is one. So lawyer for those terms will cancel. And on the left, it excuse me the right hand side, we cannot divide ever 72 or eight by seven evenly. So therefore we can leave our answer as 72 minus eight w all over seven. And now we've isolated sea and we've found that C is equal to 72 minus eight w all over seven
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