Question

1. without solving, identify whether each equation has a solution that is positive, negative, or zero.

a ( 6x = 13.6 ) b ( -3x = -9.9 )
c ( 2x = -8.2 ) d ( 2x + 5 = -5 )
e ( 4x - 2 = -2 ) f ( -6x + 2 = -10 )

1. what is the solution to the equation ( 2.5 + 8x = 4.9 - 4x )?

a. ( -0.2 )
b. ( 0.2 )
c. ( 0 )
d. no solution

1. solve each equation. show or explain your thinking.

a ( 5z - 8 + 4z - 6 = 10 - 6z - 3 ) b ( 3(3 - w) + 7w = 4w + 13 )
c ( -7y + 0.8 = 1.8 - 3y ) d ( 4(3 + 5x) - 9x = 6x + 16 + 5x - 4 )

Explanation:

Problem 1

Step1: Analyze sign of a)

Positive/positive = positive

Step2: Analyze sign of b)

Negative/negative = positive

Step3: Analyze sign of c)

Negative/positive = negative

Step4: Isolate term for d)

$2x = -5 - 5 = -10$, negative/positive = negative

Step5: Isolate term for e)

$4x = -2 + 2 = 0$, 0/positive = zero

Step6: Isolate term for f)

$-6x = -10 - 2 = -12$, negative/negative = positive

Step1: Move x terms to left

$8x + 4x = 4.9 - 2.5$

Step2: Simplify both sides

$12x = 2.4$

Step3: Solve for x

$x = \frac{2.4}{12}$

Part a

Step1: Combine like terms

$5z + 4z -8 -6 = 10 -3 -6z$
$9z -14 = 7 -6z$

Step2: Move z terms left

$9z +6z = 7 +14$
$15z = 21$

Step3: Solve for z

$z = \frac{21}{15} = \frac{7}{5}$

Part b

Step1: Expand left side

$9 -3w +7w = 4w +13$
$9 +4w = 4w +13$

Step2: Subtract 4w

$9 = 13$, which is false

Part c

Step1: Move y terms left

$-7y +3y = 1.8 -0.8$
$-4y = 1$

Step2: Solve for y

$y = -\frac{1}{4}$

Part d

Step1: Expand and combine terms

$12 +20x -9x = 6x +5x +16 -4$
$12 +11x = 11x +12$

Step2: Subtract 11x

$12 = 12$, which is always true

Answer:

a) Positive
b) Positive
c) Negative
d) Negative
e) Zero
f) Positive

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Problem 2