Photo AI

n is an integer such that 3n + 2 ≤ 14 and \( \frac{6n}{n + 5} > 1 \) Find all the possible values of n. - Edexcel - GCSE Maths - Question 1 - 2018 - Paper 2

Question icon

Question 1

n-is-an-integer-such-that-3n-+-2-≤-14-and-\(-\frac{6n}{n-+-5}->-1-\)-Find-all-the-possible-values-of-n.-Edexcel-GCSE Maths-Question 1-2018-Paper 2.png

n is an integer such that 3n + 2 ≤ 14 and \( \frac{6n}{n + 5} > 1 \) Find all the possible values of n.

Worked Solution & Example Answer:n is an integer such that 3n + 2 ≤ 14 and \( \frac{6n}{n + 5} > 1 \) Find all the possible values of n. - Edexcel - GCSE Maths - Question 1 - 2018 - Paper 2

Step 1

Solve the inequality 3n + 2 ≤ 14

96%

114 rated

Answer

To solve this inequality, we first isolate n:

  1. Subtract 2 from both sides: [ 3n \leq 12 ]
  2. Then divide by 3: [ n \leq 4 ]

So, the possible values of n from this inequality are all integers less than or equal to 4.

Step 2

Solve the inequality \( \frac{6n}{n + 5} > 1 \)

99%

104 rated

Answer

To solve ( \frac{6n}{n + 5} > 1 ):

  1. First, rearrange the inequality: [ 6n > n + 5 ]
  2. Subtract n from both sides: [ 5n > 5 ]
  3. Now divide by 5: [ n > 1 ]

Thus, the possible values of n from this inequality are integers greater than 1.

Step 3

Combine the solutions of both inequalities

96%

101 rated

Answer

Now, we combine the results:

  • From the first inequality, ( n \leq 4 )
  • From the second inequality, ( n > 1 )

The integer solutions that satisfy both inequalities are: ( n = 2, 3, 4 ).

Join the GCSE students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

Other GCSE Maths topics to explore

Number Toolkit

Maths - Edexcel

Prime Factors, HCF & LCM

Maths - Edexcel

Powers, Roots & Standard Form

Maths - Edexcel

Simple & Compound Interest, Growth & Decay

Maths - Edexcel

Fractions, Decimals & Percentages

Maths - Edexcel

Rounding, Estimation & Bounds

Maths - Edexcel

Surds

Maths - Edexcel

Algebraic Roots & Indices

Maths - Edexcel

Expanding Brackets

Maths - Edexcel

Factorising

Maths - Edexcel

Completing the Square

Maths - Edexcel

Algebraic Fractions

Maths - Edexcel

Rearranging Formulae

Maths - Edexcel

Algebraic Proof

Maths - Edexcel

Linear Equations

Maths - Edexcel

Solving Quadratic Equations

Maths - Edexcel

Simultaneous Equations

Maths - Edexcel

Iteration

Maths - Edexcel

Forming & Solving Equations

Maths - Edexcel

Functions

Maths - Edexcel

Coordinate Geometry

Maths - Edexcel

Estimating Gradients & Areas under Graphs

Maths - Edexcel

Real-Life Graphs

Maths - Edexcel

Transformations of Graphs

Maths - Edexcel

Sequences

Maths - Edexcel

Direct & Inverse Proportion

Maths - Edexcel

Standard & Compound Units

Maths - Edexcel

Exchange Rates & Best Buys

Maths - Edexcel

Geometry Toolkit

Maths - Edexcel

Angles in Polygons & Parallel Lines

Maths - Edexcel

Bearings, Scale Drawing, Constructions & Loci

Maths - Edexcel

Area & Perimeter

Maths - Edexcel

Right-Angled Triangles - Pythagoras & Trigonometry

Maths - Edexcel

Sine, Cosine Rule & Area of Triangles

Maths - Edexcel

Vectors

Maths - Edexcel

Transformations

Maths - Edexcel

Scatter Graphs & Correlation

Maths - Edexcel

Statistics

Maths - Edexcel

Ratio Analysis and Problem Solving

Maths - Edexcel

Inequalities

Maths - Edexcel

Volume, Area & Surface Area

Maths - Edexcel

The Circle

Maths - Edexcel

Probability

Maths - Edexcel

Trigonometry

Maths - Edexcel

Growth & Decay

Maths - Edexcel

Outliers

Maths - Edexcel

;