1. Equations & Inequalities

Linear Equations

1. Equations & Inequalities

Linear Equations

Struggling with College Algebra?

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Multiple Choice

Solve the equation. Then state whether it is an identity, conditional, or inconsistent equation.
$-2\left(5-3x\right)+x=7x-10$

Identity

Conditional

Inconsistent

Verified step by step guidance

Start by distributing the -2 across the terms inside the parentheses on the left side of the equation: $-2(5 - 3x)$. This results in $-2 \cdot 5 + (-2) \cdot (-3x)$, which simplifies to $-10 + 6x$.

Combine the terms on the left side of the equation: $-10 + 6x + x$. This simplifies to $-10 + 7x$.

Now, the equation is $-10 + 7x = 7x - 10$. Notice that both sides of the equation are identical.

Since both sides of the equation are identical, this means the equation is true for all values of $x$.

Therefore, the equation is an identity, as it holds true for any value of $x$.

7:48m

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Go to Practice

Struggling with College Algebra?

Solve the equation. Then state whether it is an identity, conditional, or inconsistent equation. −2(5−3x)+x=7x−10-2\left(5-3x\right)+x=7x-10−2(5−3x)+x=7x−10

Watch next

Linear Equations practice set

Solve the equation. Then state whether it is an identity, conditional, or inconsistent equation.
$-2\left(5-3x\right)+x=7x-10$