Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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