Linear equations and inequalities

2010011504

Level:

We are given the inequality \( 2x+\frac{3-4x}2 < \frac72 \). Decide which of the following inequalities is equivalent to the given inequality, i.e. which of the following inequalities was obtained from the given inequality by equivalent transformations.

\( 0\cdot x < 4 \)

\( 0\cdot x < -4\)

\( 0\cdot x > 4 \)

\( 2\cdot x > -4 \)

2010011505

Level:

Assuming \(x\in \mathbb{R}\), find the solution set of the following inequality. \[ (x+3)^2-1+3x^2 >(2-2x)^2 \]

\(\left( -\frac27;\infty\right)\)

\(\left( \frac27;\infty\right)\)

\(\left( -\infty;\frac27 \right)\)

\(\left( -\infty;-\frac27\right)\)

2010011506

Level:

Assuming \(x\in \mathbb{R}\), find the solution set of the following inequality. \[ (x-2)^2+(2+x)^2 \leq 8+2x^2 \]

\(\mathbb{R}\)

\(\emptyset \)

\([ 0;8]\)

\([ -8;0]\)

2010016201

Level:

Find the linear inequality of which the solution set is shown in red in the graph below.

\( \frac{x+4}2 > 6-x \)

\( \frac{x-4}2 > 6-x \)

\( x+2 \geq 6-x \)

\( \frac{x+4}2 < 6-x \)

2010016203

Level:

Find the minimal integer which satisfies the following inequality. \[ 3x - 1 \leq 7x-8 \]

\( 2 \)

\( 0 \)

\(3\)

\( 1 \)

2110016202

Level:

Solve the following inequality and choose the diagram that shows the correct solution set marked in red on the number line. \[ 4.5 - 0.7x < 1 - 2.1x\]