Solve each equation. (1/15)(2x+5) = (1/9)(x+2)

Question

Accepted Answer

Welcome back. I am so glad you're here. We are. Given this linear equation, we have 1/20 times three X plus eight and that's equal to 1/12 times nine X plus 13. And we're asked to solve this linear equation. Well, typically when we see a number squished up against a parentheses, we would start off by distributing those numbers to what's inside the parentheses. However, in this case the numbers squished up in front of the parentheses are fractions and not very nice fractions. So let's, for our first step, get rid of these fractions. In order to do that. We need to find the lowest common denominator and looking at 20 and 12, the lowest common denominator for those two is going to be 60. So we're going to multiply everything times 60. And that would look like this. We have 60 times 1/ times three X plus eight equal to 60 times 1, 12 times nine x plus 13. And now distributing the 62 the fractions 60 times 1/20 is 60/20 or simplified, 60 divided by 20 equals three. And that's still times the three X plus eight. That's equal to 60 times 1/12. Well, that is 60/12 and 60 divided by 12 equals five. So that's five times still the nine X plus 13 and three and five are much nicer numbers to distribute. So now taking three times three X. That's nine X plus three times eight is equals on the right hand side five times nine X is 45 X plus five times 13 is 65. Now let's bring our X terms together. Let's subtract nine X from both sides so that our X terms will be positive on the right hand side. And then let's subtract 65 from both sides. So that will bring our constant terms together on the left hand side. So on the left nine X minus nine X. Is zero. As we intended, 24 minus 65 equals a negative and then equals 45 X minus nine X equals 36 X. And then positive 65 minus 65 equals zero. As we intended, X is almost by itself. We just have it being multiplied by that 36. So now let's divide both sides by 36. To get the X by itself On the right hand side we have X equals and on the left hand side that just stays as negative 41/36 so X equals negative 41 36th. We look at our answer choices and that matches with answer choice C. Well done, we'll catch you on the next one

Solve each equation. (1/15)(2x+5) = (1/9)(x+2)

Key Concepts

Solving Linear Equations

Distributive Property

Working with Fractions in Equations

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