Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{+14}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+14}\color{blue}{-14-x } & = & 7 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 7 \color{blue}{-14} \\\Leftrightarrow &-15x & = &-7\\\Leftrightarrow & \color{red}{-15}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{15} } & & \\ & V = \left\{ \frac{7}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{+13}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & 2x \color{red}{+13}\color{blue}{-13-13x } & = & 2 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & 2x \color{blue}{-13x } & = & 2 \color{blue}{-13} \\\Leftrightarrow &-11x & = &-11\\\Leftrightarrow & \color{red}{-11}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-11}{-11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{-2}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-2}\color{blue}{+2-x } & = & -8 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -8 \color{blue}{+2} \\\Leftrightarrow &-15x & = &-6\\\Leftrightarrow & \color{red}{-15}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{+7}& = & 4 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{+7}\color{blue}{-7-5x } & = & 4 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & 4 \color{blue}{-7} \\\Leftrightarrow &-19x & = &-3\\\Leftrightarrow & \color{red}{-19}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-3}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{3}{19} } & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{+10}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+10}\color{blue}{-10-x } & = & 1 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 1 \color{blue}{-10} \\\Leftrightarrow &-4x & = &-9\\\Leftrightarrow & \color{red}{-4}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-9}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{-14}& = & -8 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-14}\color{blue}{+14+4x } & = & -8 \color{red}{ -4x }\color{blue}{+14+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -8 \color{blue}{+14} \\\Leftrightarrow &13x & = &6\\\Leftrightarrow & \color{red}{13}x & = &6\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{6}{13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{-6}& = & -2 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{-6}\color{blue}{+6+10x } & = & -2 \color{red}{ -10x }\color{blue}{+6+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & -2 \color{blue}{+6} \\\Leftrightarrow &21x & = &4\\\Leftrightarrow & \color{red}{21}x & = &4\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{4}{21} \\\Leftrightarrow & \color{green}{ x = \frac{4}{21} } & & \\ & V = \left\{ \frac{4}{21} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{+11}& = & 2 \color{red}{ +10x } \\\Leftrightarrow & 3x \color{red}{+11}\color{blue}{-11-10x } & = & 2 \color{red}{ +10x }\color{blue}{-11-10x } \\\Leftrightarrow & 3x \color{blue}{-10x } & = & 2 \color{blue}{-11} \\\Leftrightarrow &-7x & = &-9\\\Leftrightarrow & \color{red}{-7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{+4}& = & -9 \color{red}{ -5x } \\\Leftrightarrow & 8x \color{red}{+4}\color{blue}{-4+5x } & = & -9 \color{red}{ -5x }\color{blue}{-4+5x } \\\Leftrightarrow & 8x \color{blue}{+5x } & = & -9 \color{blue}{-4} \\\Leftrightarrow &13x & = &-13\\\Leftrightarrow & \color{red}{13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-13}{13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+5}& = & 13 \color{red}{ +10x } \\\Leftrightarrow & 7x \color{red}{+5}\color{blue}{-5-10x } & = & 13 \color{red}{ +10x }\color{blue}{-5-10x } \\\Leftrightarrow & 7x \color{blue}{-10x } & = & 13 \color{blue}{-5} \\\Leftrightarrow &-3x & = &8\\\Leftrightarrow & \color{red}{-3}x & = &8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{-1}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-1}\color{blue}{+1-x } & = & 12 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 12 \color{blue}{+1} \\\Leftrightarrow &5x & = &13\\\Leftrightarrow & \color{red}{5}x & = &13\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{13}{5} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{-8}& = & 12 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-8}\color{blue}{+8-6x } & = & 12 \color{red}{ +6x }\color{blue}{+8-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & 12 \color{blue}{+8} \\\Leftrightarrow &-11x & = &20\\\Leftrightarrow & \color{red}{-11}x & = &20\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{20}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{11} } & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)