Question

How do you solve this absolute value Q.2{5g+3π}=234

Answer 1

2(5g+3p)=234

Geometric figure: Straight Line

Slope = -3.333/2.000 = -1.667
g-intercept = 117/5 = 23.40000
p-intercept = 117/3 = 39
Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

2*(5*g+3*p)-(234)=0

Step by step solution :

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Step 1 :

Equation at the end of step 1 :

2 • (5g + 3p) - 234 = 0
Step 2 :

Step 3 :

Pulling out like terms :

3.1 Pull out like factors :

10g + 6p - 234 = 2 • (5g + 3p - 117)

Equation at the end of step 3 :

2 • (5g + 3p - 117) = 0
Step 4 :

Equations which are never true :

4.1 Solve : 2 = 0

This equation has no solution.
A a non-zero constant never equals zero.

Equation of a Straight Line

4.2 Solve 5g+3p-117 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 5g+3p-117 = 0 and calculate its properties

Graph of a Straight Line :



Calculate the Y-Intercept :

Notice that when g = 0 the value of p is 39/1 so this line "cuts" the p axis at p=39.00000

p-intercept = 117/3 = 39
Calculate the X-Intercept :

When p = 0 the value of g is 117/5 Our line therefore "cuts" the g axis at g=23.40000

g-intercept = 117/5 = 23.40000
Calculate the Slope :

Slope is defined as the change in p divided by the change in g. We note that for g=0, the value of p is 39.000 and for g=2.000, the value of p is 35.667. So, for a change of 2.000 in g (The change in g is sometimes referred to as "RUN") we get a change of 35.667 - 39.000 = -3.333 in p. (The change in p is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = -3.333/2.000 = -1.667
Geometric figure: Straight Line

Slope = -3.333/2.000 = -1.667
g-intercept = 117/5 = 23.40000
p-intercept = 117/3 = 39

Answer 2

Absolute values are generally written as || instead of {}

|x| = 1 is the equivalent of 2 equations
x=1 and x=-1