Problem solving with linear inequalities | Maths | Quizalize & Oak National Academy

Starter quiz

$15x+25y=1500$ is an equation whereas $15x+25y<1500$ is an ______.

'inequality' ✓
Which of these is the point of intersection of these two linear equations?

$(0, 0)$

$(0, 4)$

$(4, 0)$

$(4, 12)$ ✓

$(12, 4)$
For the equation $c=10+6m$ what is the value of $c$ when $m=9$ ? $c=$ ______.

'64' ✓
Solve $5x .$

$x>7$

$x<7$ ✓

$x<28$

$x<5$

$x>5$
Which of these values satisfy this inequality? ${3x+6y}\le{450}$

$(60,30)$ ✓

$(30,60)$ ✓

$(70,20)$ ✓

$(20,70)$

$(60,50)$
A taxi firm charge a fixed rate of $\pounds4$ per journey plus $\pounds1.50$ per mile travelled. The cost of your journey cannot exceed $\pounds16$ . Which inequality models this scenario?

$4m+1.5<16$

$4+1.5m<16m$

$4+1.5m<16$

${4+1.5m}\le16$ ✓

${4m+1.5}\le16$

Exit quiz

The graph shows the charges of three taxi firms. The coordinate pair $(3,9)$ is the point of __________ of the graphs of taxi firms 'a' and 'b'.

intersection ✓

intercept

inequality
In what region does taxi firm 'a' charge less than taxi firm 'b'?

$m<3$ ✓

$m>3$

$m\le3$

$m<4$

$m>4$
In what region does taxi firm 'c' charge less than taxi firm 'a'?

$m<4$

$m>4$ ✓

$m\geq4$

$m<8$

$m>8$
These inequalities model a company's packaging and production constraints. Which of these points satisfies the production constraint but not the packaging constraint?

$(10, 80)$

$(60, 80)$

$(60, 10)$ ✓

$(10, 10)$
These inequalities model a company's packaging and production constraints. Which of these points satisfy both the production and the packaging constraints?

$(50,15)$ ✓

$(15,50)$

$(40,30)$

$(30,40)$

$(60,0)$ ✓
These inequalities model a company's packaging and production constraints. Which coordinate pair is the point where both production and packaging are optimised? ______

'(50,20)' ✓

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Lesson Details

Key learning points

When handling a project, there are often constraints
Constraints exist for a variety of reasons, such as cost or supply limitations
Finding a set of possible solutions allows you to work within the constraints

Common misconception

We are only interested in points that are in the region satisfied by all inequalities.

With practical contexts, such as project management, it is useful to know when one constraint is not being met as it can suggest where additional resources (if available) should be allocated.

Keywords

Inequality - An inequality is used to show that one expression may not be equal to another.