Question Video: Evaluating Algebraic Expressions after Solving Linear Equations | Nagwa Question Video: Evaluating Algebraic Expressions after Solving Linear Equations | Nagwa

Question Video: Evaluating Algebraic Expressions after Solving Linear Equations Mathematics • First Year of Preparatory School

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Given that 6𝑥 + 8𝑥 + 3𝑥 + 9𝑥 = 130, find the value of 3𝑥 + 6.

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Video Transcript

Given that six 𝑥 plus eight 𝑥 plus three 𝑥 plus nine 𝑥 equals 130, find the value of three 𝑥 plus six.

In this question, we’re actually given two things. First of all, we have an equation which we’re gonna solve to find a value of 𝑥. And secondly, we have an expression. And it’s this expression that we need to find the value of. And we’re gonna be able to do that once we know what 𝑥 is by solving our first equation. So we’re gonna start straight away by doing that.

So we have six 𝑥 plus eight 𝑥 plus three 𝑥 plus nine 𝑥 equals 130. So the first stage is to actually collect like terms. So we calculate all of our 𝑥 terms together. So we get six plus eight is 14 plus another three is 17 plus nine is 26𝑥. And this is equal to 130.

Okay, we’re now in a position where we can actually solve to find 𝑥. And to do this, we’re gonna divide both sides by 26. But 𝑥 is equal to 130 over 26. So therefore, we can say that 𝑥 is equal to five. And we can use this now to find out the value of our expression. And to enable us to do this, we’re gonna actually to substitute our value 𝑥 equals five into our expression three 𝑥 plus six, which gives us three multiplied by five plus six.

And that’s because we substituted five in place of our 𝑥 which is equal to 21. We can now say that three 𝑥 plus six is equal to 21 when 𝑥 equals five. And that’s answered our question that says that “given that six 𝑥 plus eight 𝑥 plus three 𝑥 plus nine 𝑥 equals 130, find the value of three 𝑥 plus six.”

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