Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{-7}& = & 7 \color{red}{ +2x } \\\Leftrightarrow & -x \color{red}{-7}\color{blue}{+7-2x } & = & 7 \color{red}{ +2x }\color{blue}{+7-2x } \\\Leftrightarrow & -x \color{blue}{-2x } & = & 7 \color{blue}{+7} \\\Leftrightarrow &-3x & = &14\\\Leftrightarrow & \color{red}{-3}x & = &14\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{14}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{3} } & & \\ & V = \left\{ \frac{-14}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+11}& = & 14 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{+11}\color{blue}{-11-3x } & = & 14 \color{red}{ +3x }\color{blue}{-11-3x } \\\Leftrightarrow & 8x \color{blue}{-3x } & = & 14 \color{blue}{-11} \\\Leftrightarrow &5x & = &3\\\Leftrightarrow & \color{red}{5}x & = &3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{-15}& = & 10 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15+6x } & = & 10 \color{red}{ -6x }\color{blue}{+15+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & 10 \color{blue}{+15} \\\Leftrightarrow &13x & = &25\\\Leftrightarrow & \color{red}{13}x & = &25\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{25}{13} \\\Leftrightarrow & \color{green}{ x = \frac{25}{13} } & & \\ & V = \left\{ \frac{25}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{-14}& = & 6 \color{red}{ +5x } \\\Leftrightarrow & 8x \color{red}{-14}\color{blue}{+14-5x } & = & 6 \color{red}{ +5x }\color{blue}{+14-5x } \\\Leftrightarrow & 8x \color{blue}{-5x } & = & 6 \color{blue}{+14} \\\Leftrightarrow &3x & = &20\\\Leftrightarrow & \color{red}{3}x & = &20\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{20}{3} \\\Leftrightarrow & \color{green}{ x = \frac{20}{3} } & & \\ & V = \left\{ \frac{20}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{-7}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-7}\color{blue}{+7-x } & = & -8 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -8 \color{blue}{+7} \\\Leftrightarrow &-4x & = &-1\\\Leftrightarrow & \color{red}{-4}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{-10}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-10}\color{blue}{+10-x } & = & 5 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 5 \color{blue}{+10} \\\Leftrightarrow &-16x & = &15\\\Leftrightarrow & \color{red}{-16}x & = &15\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{15}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{16} } & & \\ & V = \left\{ \frac{-15}{16} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{-10}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-10}\color{blue}{+10-x } & = & 2 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 2 \color{blue}{+10} \\\Leftrightarrow &-3x & = &12\\\Leftrightarrow & \color{red}{-3}x & = &12\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{12}{-3} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{+10}& = & -12 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+10}\color{blue}{-10-9x } & = & -12 \color{red}{ +9x }\color{blue}{-10-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -12 \color{blue}{-10} \\\Leftrightarrow &5x & = &-22\\\Leftrightarrow & \color{red}{5}x & = &-22\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-22}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{5} } & & \\ & V = \left\{ \frac{-22}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{+2}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+2}\color{blue}{-2-x } & = & 14 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 14 \color{blue}{-2} \\\Leftrightarrow &-12x & = &12\\\Leftrightarrow & \color{red}{-12}x & = &12\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{12}{-12} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{-8}& = & -4 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{-8}\color{blue}{+8-4x } & = & -4 \color{red}{ +4x }\color{blue}{+8-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & -4 \color{blue}{+8} \\\Leftrightarrow &-19x & = &4\\\Leftrightarrow & \color{red}{-19}x & = &4\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{4}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{19} } & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{-11}& = & 12 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{-11}\color{blue}{+11-6x } & = & 12 \color{red}{ +6x }\color{blue}{+11-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & 12 \color{blue}{+11} \\\Leftrightarrow &-x & = &23\\\Leftrightarrow & \color{red}{-}x & = &23\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{23}{-1} \\\Leftrightarrow & \color{green}{ x = -23 } & & \\ & V = \left\{ -23 \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{-2}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-2}\color{blue}{+2-x } & = & -8 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -8 \color{blue}{+2} \\\Leftrightarrow &-6x & = &-6\\\Leftrightarrow & \color{red}{-6}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-6}{-6} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)