Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(-9x-12=-14+7x\)
2. \(14x-4=11-13x\)
3. \(8x+4=13-7x\)
4. \(-5x-15=6+x\)
5. \(5x-6=-6+9x\)
6. \(11x-10=2+7x\)
7. \(11x+3=2-2x\)
8. \(2x+2=-12+7x\)
9. \(5x-9=-7-2x\)
10. \(-15x-2=-14+4x\)
11. \(10x-8=-12+9x\)
12. \(-14x-7=-7+x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{-12}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{-12}\color{blue}{+12-7x } & = & -14 \color{red}{ +7x }\color{blue}{+12-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & -14 \color{blue}{+12} \\\Leftrightarrow &-16x & = &-2\\\Leftrightarrow & \color{red}{-16}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-2}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{-4}& = & 11 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-4}\color{blue}{+4+13x } & = & 11 \color{red}{ -13x }\color{blue}{+4+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 11 \color{blue}{+4} \\\Leftrightarrow &27x & = &15\\\Leftrightarrow & \color{red}{27}x & = &15\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{15}{27} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{+4}& = & 13 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+4}\color{blue}{-4+7x } & = & 13 \color{red}{ -7x }\color{blue}{-4+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 13 \color{blue}{-4} \\\Leftrightarrow &15x & = &9\\\Leftrightarrow & \color{red}{15}x & = &9\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{9}{15} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{-15}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-15}\color{blue}{+15-x } & = & 6 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 6 \color{blue}{+15} \\\Leftrightarrow &-6x & = &21\\\Leftrightarrow & \color{red}{-6}x & = &21\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{21}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{-6}& = & -6 \color{red}{ +9x } \\\Leftrightarrow & 5x \color{red}{-6}\color{blue}{+6-9x } & = & -6 \color{red}{ +9x }\color{blue}{+6-9x } \\\Leftrightarrow & 5x \color{blue}{-9x } & = & -6 \color{blue}{+6} \\\Leftrightarrow &-4x & = &0\\\Leftrightarrow & \color{red}{-4}x & = &0\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{0}{-4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{-10}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & 11x \color{red}{-10}\color{blue}{+10-7x } & = & 2 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & 11x \color{blue}{-7x } & = & 2 \color{blue}{+10} \\\Leftrightarrow &4x & = &12\\\Leftrightarrow & \color{red}{4}x & = &12\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{12}{4} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{+3}& = & 2 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{+3}\color{blue}{-3+2x } & = & 2 \color{red}{ -2x }\color{blue}{-3+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & 2 \color{blue}{-3} \\\Leftrightarrow &13x & = &-1\\\Leftrightarrow & \color{red}{13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+2}& = & -12 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{+2}\color{blue}{-2-7x } & = & -12 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & -12 \color{blue}{-2} \\\Leftrightarrow &-5x & = &-14\\\Leftrightarrow & \color{red}{-5}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-14}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{14}{5} } & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{-9}& = & -7 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{-9}\color{blue}{+9+2x } & = & -7 \color{red}{ -2x }\color{blue}{+9+2x } \\\Leftrightarrow & 5x \color{blue}{+2x } & = & -7 \color{blue}{+9} \\\Leftrightarrow &7x & = &2\\\Leftrightarrow & \color{red}{7}x & = &2\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{2}{7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{-2}& = & -14 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{-2}\color{blue}{+2-4x } & = & -14 \color{red}{ +4x }\color{blue}{+2-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & -14 \color{blue}{+2} \\\Leftrightarrow &-19x & = &-12\\\Leftrightarrow & \color{red}{-19}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-12}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{12}{19} } & & \\ & V = \left\{ \frac{12}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{-8}& = & -12 \color{red}{ +9x } \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8-9x } & = & -12 \color{red}{ +9x }\color{blue}{+8-9x } \\\Leftrightarrow & 10x \color{blue}{-9x } & = & -12 \color{blue}{+8} \\\Leftrightarrow &x & = &-4\\\Leftrightarrow & \color{red}{}x & = &-4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -4 \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{-7}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-7}\color{blue}{+7-x } & = & -7 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -7 \color{blue}{+7} \\\Leftrightarrow &-15x & = &0\\\Leftrightarrow & \color{red}{-15}x & = &0\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{0}{-15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)