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If (ax + 2)(bx + 7) = 15(x 2) + cx + 14 for all values of x, and a + b = 8 then the two possible values for c is 31 and 41.
A linear equation is an algebraic equation with only a constant and a first-order (linear) term of the form y = mx + b, where m is the slope and b is the y-intercept. The above is sometimes referred to as a "linear equation of two variables," where y and x are the variables.
Let the equation be
(ax + 2)(bx + 7) = 15 + cx + 14
(ax + 2)(bx + 7) = ab + 7ax + 2bx + 14 = ab
+ (7a + 2b) + 14
On comparing both equations
ab = 15 ------ (1)
7a + 2b = c -------(2)
Also, it is given that a + b = 8 --------(3)
From equations (1) and (3) it can be observe that either a or b equal to 3 or 5
From equation (2),
When a = 3 and b = 5, then c = 7(3) + 2(5) = 21 + 10 = 31
When a = 5 and b = 3, then c = 7(5) + 2(3) = 35 + 6 = 41
Therefore, the correct answer is option D) 31 and 41
To learn more about linear equation, refer to:
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Answer:
Step 1:
We need to place the numbers in descending order of the power. Here, has the largest power, so that number goes first. We keep doing this until we end up with our final expression, placed in order based on the powers.
Step 2:
We can see that the last three numbers, 17, -7, and 6, don't have variables or powers, so we simplify by adding (and subtracting) them.
Our final equation: