Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{-11}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-11}\color{blue}{+11-x } & = & 5 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 5 \color{blue}{+11} \\\Leftrightarrow &-3x & = &16\\\Leftrightarrow & \color{red}{-3}x & = &16\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{16}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{3} } & & \\ & V = \left\{ \frac{-16}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{+15}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+15}\color{blue}{-15-x } & = & 3 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 3 \color{blue}{-15} \\\Leftrightarrow &-10x & = &-12\\\Leftrightarrow & \color{red}{-10}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-12}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{+1}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+1}\color{blue}{-1+11x } & = & -7 \color{red}{ -11x }\color{blue}{-1+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -7 \color{blue}{-1} \\\Leftrightarrow &23x & = &-8\\\Leftrightarrow & \color{red}{23}x & = &-8\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-8}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{23} } & & \\ & V = \left\{ \frac{-8}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{+9}& = & -13 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+9}\color{blue}{-9+9x } & = & -13 \color{red}{ -9x }\color{blue}{-9+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & -13 \color{blue}{-9} \\\Leftrightarrow &19x & = &-22\\\Leftrightarrow & \color{red}{19}x & = &-22\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-22}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{19} } & & \\ & V = \left\{ \frac{-22}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{+6}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & 5x \color{red}{+6}\color{blue}{-6-13x } & = & -12 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & 5x \color{blue}{-13x } & = & -12 \color{blue}{-6} \\\Leftrightarrow &-8x & = &-18\\\Leftrightarrow & \color{red}{-8}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-18}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{+13}& = & 15 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+13}\color{blue}{-13-10x } & = & 15 \color{red}{ +10x }\color{blue}{-13-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & 15 \color{blue}{-13} \\\Leftrightarrow &-19x & = &2\\\Leftrightarrow & \color{red}{-19}x & = &2\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{2}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{19} } & & \\ & V = \left\{ \frac{-2}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{+10}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+10}\color{blue}{-10-x } & = & 13 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 13 \color{blue}{-10} \\\Leftrightarrow &x & = &3\\\Leftrightarrow & \color{red}{}x & = &3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 3 \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{-7}& = & -8 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-7}\color{blue}{+7+5x } & = & -8 \color{red}{ -5x }\color{blue}{+7+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -8 \color{blue}{+7} \\\Leftrightarrow &11x & = &-1\\\Leftrightarrow & \color{red}{11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{+13}& = & 9 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+13}\color{blue}{-13+9x } & = & 9 \color{red}{ -9x }\color{blue}{-13+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & 9 \color{blue}{-13} \\\Leftrightarrow &19x & = &-4\\\Leftrightarrow & \color{red}{19}x & = &-4\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-4}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{19} } & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+7}& = & 11 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{+7}\color{blue}{-7-4x } & = & 11 \color{red}{ +4x }\color{blue}{-7-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & 11 \color{blue}{-7} \\\Leftrightarrow &-19x & = &4\\\Leftrightarrow & \color{red}{-19}x & = &4\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{4}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{19} } & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{+5}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{+5}\color{blue}{-5-11x } & = & 14 \color{red}{ +11x }\color{blue}{-5-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & 14 \color{blue}{-5} \\\Leftrightarrow &-3x & = &9\\\Leftrightarrow & \color{red}{-3}x & = &9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{9}{-3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{-9}& = & -2 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-9}\color{blue}{+9-11x } & = & -2 \color{red}{ +11x }\color{blue}{+9-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -2 \color{blue}{+9} \\\Leftrightarrow &x & = &7\\\Leftrightarrow & \color{red}{}x & = &7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 7 \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)