Let's solve your equation step-by-step.<span><span><span>6x</span>−<span>2<span>x4</span></span></span>=<span>12x</span></span><span><span><span>−<span>2<span>x4</span></span></span>+<span>6x</span></span>=<span>12x</span></span>
Step 1: Subtract 12x from both sides.<span><span><span><span>−<span>2<span>x4</span></span></span>+<span>6x</span></span>−<span>12x</span></span>=<span><span>12x</span>−<span>12x</span></span></span><span><span><span>−<span>2<span>x4</span></span></span>−<span>6x</span></span>=0</span>
Step 2: Factor left side of equation.<span><span><span>2x</span><span>(<span><span>−<span>x3</span></span>−3</span>)</span></span>=0</span>
Step 3: Set factors equal to 0.<span><span><span>2x</span>=<span><span><span>0<span> or </span></span>−<span>x3</span></span>−3</span></span>=0</span><span><span>x=<span><span>0<span> or </span></span>x</span></span>=<span>−1.44225</span></span>
Answer:<span><span>x=<span><span>0<span> or </span></span>x</span></span>=<span>−1.44225 This is the answer if its exponent. The other might be:</span></span>
Step 1: Simplify both sides of the equation.<span><span><span>6x</span>−<span>2<span>(<span>4x</span>)</span></span></span>=<span>12x</span></span><span>
Simplify: (Show steps)</span><span><span>−<span>2x</span></span>=<span>12x</span></span>
Step 2: Subtract 12x from both sides.<span><span><span>−<span>2x</span></span>−<span>12x</span></span>=<span><span>12x</span>−<span>12x</span></span></span><span><span>−<span>14x</span></span>=0</span>
Step 3: Divide both sides by -14.<span><span><span>−<span>14x</span></span><span>−14</span></span>=<span>0<span>−14</span></span></span><span>x=<span>0
You never specified what the (x4) part was so I gave both.</span></span>
<h2>SOLVING</h2>
Find the equation of the line, with the info given.
The formula used in this problem is,
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| simplify
There is only one solution
Well, if a line is parallel to another, they share the same slope. Why that is, I can further explain in the comments if you're interested. Anyway, because we know this line is parallel to 3x-5, it MUST have a slope of 3, since that is the slope of the other line. So you can go ahead and mark out those last 3 answers. You could also mark out the first one since it's the EXACT SAME line as the one were given, so it wouldn't be parallel, it would just be equal to it. So we know the answer has to be B. What if A wasn't the same as the line given though? in that case, we could look at the point you're given. it describes the y intercept of our unknown line, since the point occurs at x=0. If that doesn't make sense, let me know and I can elaborate on why that is. Anyway, if we're looking at the general form of a line, y = mx + b, b describes the y value at which the y-intercept occurs. the y intercept were given occurs at y= 7, so the b value of our line must be 7. This agrees with answer B.
Hope that helps, and let me know if you have any questions! :)