Given wx=7x+7 and wy=4x+16 what is mwx?
Understand the Problem
The question is asking us to find the value of mwx given the equations wx = 7x + 7 and wy = 4x + 16. We will likely need to manipulate these equations to determine the relationship between mwx and the variables given.
Answer
$$ mwx = \frac{m(7wy - 84)}{4} $$
Answer for screen readers
$$ mwx = \frac{m(7wy - 84)}{4} $$
Steps to Solve
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Rewrite the given equations We need to isolate $wx$ and $wy$ from the equations provided. The equations are: $$ wx = 7x + 7 $$ $$ wy = 4x + 16 $$
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Relate $wx$ and $wy$ We can rewrite the first equation ($wx$) and the second equation ($wy$) in terms of each other. Notice both equations contain $x$.
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Substituting $x$ From the equation for $wy$, we rearrange to solve for $x$: $$ wy - 16 = 4x $$ Divide both sides by 4: $$ x = \frac{wy - 16}{4} $$
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Substitute $x$ into $wx$ Now substitute this expression for $x$ into the equation for $wx$: $$ wx = 7\left(\frac{wy - 16}{4}\right) + 7 $$
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Simplify the expression Now we simplify the expression: $$ wx = \frac{7(wy - 16)}{4} + 7 $$ $$ wx = \frac{7wy - 112}{4} + 7 $$ To combine, express 7 with a denominator of 4: $$ wx = \frac{7wy - 112 + 28}{4} $$ $$ wx = \frac{7wy - 84}{4} $$
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Find $mwx$ The variable $m$ times $wx$ becomes: $$ mwx = m \cdot \frac{7wy - 84}{4} $$
This gives us the final expression for $mwx$.
$$ mwx = \frac{m(7wy - 84)}{4} $$
More Information
The result shows how $mwx$ is expressed in terms of $wy$. This represents a linear relationship where you can see how $m$, being a multiplier, affects the value of $wx$.
Tips
A common mistake could be failing to properly distribute terms when substituting values. Make sure to carefully distribute any coefficients to maintain the integrity of the calculations.
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