How many times do you apply the distributive property in this example: 2(x + 5) – 3(2x + 7) ?
1 answer:
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We look for constants <em>a</em> and <em>b</em> such that
Rewrite all terms with a common denominator and set the numerators equal:
Then
<em>a</em> + 2<em>b</em> = 7
-2<em>a</em> - <em>b</em> = -8
Solve for <em>a</em> and <em>b</em>. Using elimination: multiply the first equation by 2 and add it to the second equation:
2 (<em>a</em> + 2<em>b</em>) + (-2<em>a</em> - <em>b</em>) = 2(7) + (-8)
2<em>a</em> + 4<em>b</em> - 2<em>a</em> - <em>b</em> = 14 - 8
3<em>b</em> = 6
<em>b</em> = 2
Then
<em>a</em> + 2(2) = 7 ==> <em>a</em> = 3
and so