1. 4/x = 5/7
2. 3a/7 = -2/5
3. x+1/6 = 4/3
4. 24/x-3 = 72/x+3
Thanks.
I'll only solve the 1st one, I think you can do the rest.
$\displaystyle \frac{4}{x} = \frac{5}{7}$
Multiply both sides by $\displaystyle x$,
$\displaystyle \frac{4}{x}\cdot x = \frac{5}{7}\cdot x$
$\displaystyle \frac{4}{\not x}\cdot \not x = \frac{5x}{7}$
$\displaystyle 4 = \frac{5x}{7}$
Now multiply both sides by $\displaystyle 7$,
$\displaystyle 4\cdot 7 = \frac{5x}{7}\cdot 7$
$\displaystyle 28 = \frac{5x}{\not 7}\cdot \not7$
$\displaystyle 28 = 5x$
$\displaystyle x = \frac{28}{5}$
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If you have an equation in the from $\displaystyle \frac{a}{b} = \frac{c}{d}$, products of the terms crosswise are equal, $\displaystyle a\cdot d = b \cdot c$
So, $\displaystyle \frac{4}{x} = \frac{5}{7}$
$\displaystyle 4\cdot 7 = 5\cdot x$
$\displaystyle 5x = 28$
$\displaystyle x = \frac{28}{5}$
Initial Equation
$\displaystyle \frac 4x = \frac 57$
You want to get x in the numerator so multiply both sides by x
$\displaystyle \frac x1 * \frac 4x = \frac 57*\frac x1$
Simplifly
$\displaystyle 4 = \frac {5x}7$
You want x to be by itself, so you need to get rid of the 7 in the denominator. You can do this by multiplying both sides by 7 since 7/7 =1
$\displaystyle \frac 71 *\frac 41 = \frac {5x}7*\frac 71$
Simplify
$\displaystyle 28 = 5x$
You want to get x by itself, so you need to get rid of the 5, do this by multiplying both sides by 1/5 since 5/5=1
$\displaystyle \frac 15*28 = 5x\frac 15$
Simplify
$\displaystyle \frac{28}5 = x$
Initial equation
$\displaystyle \frac {24}{x-3} = \frac{72}{x+3}$
Again, you need to get x out of the denominator, so multiply both sides by x-3
$\displaystyle 24 = \frac{72(x-3)}{x+3}$
X is still in the denominator on the right side, so multiply both sides by x+3
$\displaystyle 24(x+3) = 72(x-3)$
Distribute the coefficients
$\displaystyle 24x+72 = 72x-216$
You need all your x's to be on the same side, so subtract 24x
$\displaystyle 72 = 72x-24x-216$
Simplify
$\displaystyle 72 = 48x-216$
You need all the other numbers to be on the other side of x, so add 216
$\displaystyle 72 +216= 48x$
Simplify
$\displaystyle 288= 48x$
You need x to be by itself, so multiply by 1/48
$\displaystyle \frac{288}{48}= x$
And simplify
$\displaystyle 6 = x$