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Solve the following equation - Junior Cycle Mathematics - Question 7 - 2016
Question 7
Solve the following equation. $$\frac{2x+4}{3} - \frac{5x-7}{2} = 5$$ Graph each of the following inequalities on the number line given. (i) $x < 4$, where $x \in... show full transcript
Worked Solution & Example Answer:Solve the following equation - Junior Cycle Mathematics - Question 7 - 2016
Step 1
Solve the equation: $$\frac{2x+4}{3} - \frac{5x-7}{2} = 5$$
Answer
To solve the equation, first eliminate the fractions by finding a common denominator. The common denominator of 3 and 2 is 6. Multiply the entire equation by 6:
This simplifies to:
Expanding both sides:
Combine like terms:
Now, isolate x:
Dividing both sides by -11:
Thus, the solution is: or equivalent.
Step 2
Graph each of the following inequalities on the number line given. (i) $x < 4$, where $x \in \mathbb{N}$.
Answer
To graph the inequality where (natural numbers), we plot the points:
- Circle the number 4 (not included) and shade to the left:
-5 -4 -3 -2 -1 0 1 2 3 4 5
(--------------------->
This shows that the values can be 1, 2, or 3.
Step 3
Graph each of the following inequalities on the number line given. (ii) $x < 4$, where $x \in \mathbb{Z}$.
Answer
For the inequality where (integers), we circle 4 (not included) and shade to the left:
-5 -4 -3 -2 -1 0 1 2 3 4 5
(====================>
This indicates that included integers are -5, -4, -3, -2, -1, 0, 1, 2, and 3.
Step 4
Graph each of the following inequalities on the number line given. (iii) $x < 4$, where $x \in \mathbb{R}$.
Answer
In this graph for where (real numbers), we again circle the number 4 (not included) and shade all values to the left:
-5 -4 -3 -2 -1 0 1 2 3 4 5
(====================>
This demonstrates that all real numbers less than 4 are included.