In Exercises 57–60, solve each equation for x.

Question

Accepted Answer

Welcome back. I am so glad you're here. We are asked to solve for X. And it's here inside of this matrix and we are actually going to solve for X inside the matrix by figuring out the determinant of that matrix and then setting it equal to negative 20. So let's figure out the determinant. We have got a two x two matrix. I'll copy that down. eight and X is the first column and the second column is two negative three. Now we recall from previous lessons on determinants, we're going to take the number in the upper left hand corner and multiply it by the number in the bottom right hand corner. So eight times negative three is negative and then we're going to take the term in the bottom left and multiply it by the term in the upper right. So that's X times two or two X. And now we are going to take these two terms and subtract them. So it'll be a negative 24 minus two X. And those aren't like terms. So we actually can't combine them. And now that's as simplified as our determinant is going to get So we set that equal to negative 20. and to solve for X. Now we can add 24 to both sides and on the left will have negative two X. And on the right, that will be four and we can divide both sides by negative two. And on the left we have X equals yea that's what we want and four divided by negative two is negative two and we've solved for X. X equals negative two. We look at our answer choices and that matches with answer choice B. Well done, we'll catch on the next one.

In Exercises 57–60, solve each equation for x.

Key Concepts

Determinant of a 2x2 Matrix

Setting up and Solving Algebraic Equations

Properties of Absolute Value and Determinants

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