Solve the given linear equation, then check your answer. 1 2 = 3 4 x \frac12=\frac34x

Here we're asked to solve the given linear equation and then check your answer. The equation we're given here is one half equals three fourths x. Now we've been dealing with fraction coefficients, but we haven't always seen fractions on the other side of our equation. Don't let this freak you out, we're still going to solve this the same exact way. Because our goal here is to get this x all by itself and it's being multiplied by a fraction, we can cancel that fraction out by multiplying by its reciprocal. Remember, we're focusing on the fraction that is multiplying our variable, not any other fractions going on in our equation. So we wanna take the reciprocal of this fraction, three fourths, and multiply by it. Flipping that will give us four thirds. If I multiply by four thirds on one side of my equation, I have to multiply by four thirds on the other. So multiplying four thirds by one half over here. This three fourths and four thirds will cancel on that side, leaving me with just x, but then I have four thirds times one half. So I'm multiplying my numerators across and my denominators across. Four times one in the top will give me four. Then I have three times two on the bottom, that gives me six. So I get that four sixths is equal to x. Now you'll typically wanna go ahead and simplify your fractions as much as possible. Four third or four sixths actually simplifies to two thirds if we divide both of those values by two. So I get that two thirds is equal to x, and this is my final answer. We can, of course, check this answer by plugging it back into our original equation. So one half equals three fourths times two thirds. We're checking, is this going to give us a true statement? So keeping that one half the same over here, on this side, we're gonna do our multiplication across with our numerators, across with our denominators. Three times two will give me six. Then on the bottom, four times three will give me 12. So six over 12, that's one half if I simplify that fraction. So this ends up giving me here one half equals one half, which is definitely a true statement. So I know that I solved this correctly and two thirds equals x is my solution. I'll see you in the next one.

2. Linear Equations and Inequalities

The Multiplication and Division Properties of Equality

Beginning & Intermediate Algebra

2. Linear Equations and Inequalities

The Multiplication and Division Properties of Equality

Struggling with Beginning & Intermediate Algebra?

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Multiple Choice

Solve the given linear equation, then check your answer.
$\frac{1}{2} = \frac{3}{4} x$

$x=\frac38$

$x=2$

$x=\frac23$

$x=\frac13$

Verified step by step guidance

Start with the given equation: $\frac{1}{2} = \frac{3}{4}x$.

To isolate $x$, divide both sides of the equation by $\frac{3}{4}$. This is equivalent to multiplying both sides by the reciprocal of $\frac{3}{4}$, which is $\frac{4}{3}$.

Rewrite the equation after multiplying both sides by $\frac{4}{3}$: $x = \frac{1}{2} \times \frac{4}{3}$.

Multiply the numerators together and the denominators together: $x = \frac{1 \times 4}{2 \times 3}$.

Simplify the fraction by dividing numerator and denominator by their greatest common divisor to find the value of $x$.

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Struggling with Beginning & Intermediate Algebra?

Solve the given linear equation, then check your answer.12=34x\frac12=\frac34x

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Solve the given linear equation, then check your answer.
$\frac{1}{2} = \frac{3}{4} x$