To find an equation equivalent to the given equation [tex]\(-4(x-5)+8x=9x-3\)[/tex], let's simplify and solve it step-by-step.
1. Start by distributing and simplifying the left side of the equation [tex]\(-4(x-5) + 8x\)[/tex].
[tex]\[ -4(x - 5) + 8x \][/tex]
[tex]\[ = -4x + 20 + 8x \][/tex]
[tex]\[ = 4x + 20 \][/tex]
2. The right side of the equation is already simplified:
[tex]\[ 9x - 3 \][/tex]
3. Now we have the equation in the form:
[tex]\[ 4x + 20 = 9x - 3 \][/tex]
4. To isolate [tex]\(x\)[/tex], first move all terms involving [tex]\(x\)[/tex] to one side and constant terms to the other. Subtract [tex]\(4x\)[/tex] from both sides:
[tex]\[ 4x + 20 - 4x = 9x - 3 - 4x \][/tex]
[tex]\[ 20 = 5x - 3 \][/tex]
5. Next, add 3 to both sides to solve for [tex]\(5x\)[/tex]:
[tex]\[ 20 + 3 = 5x - 3 + 3 \][/tex]
[tex]\[ 23 = 5x \][/tex]
6. Finally, we can write the simplified equivalent equation as:
[tex]\[ 5x = 23 \][/tex]
Upon reviewing the provided options, it appears we did not achieve a match within the options. Assuming there might have been an error in either presenting the options or the original equation, you should go back to carefully restate or reconstruct the problem at hand. However, following our steps above consistently yields:
None of the provided options A, B, C, or D correctly represent the equivalent equation 5x = 23.
