Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{+14}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+14}\color{blue}{-14-x } & = & -9 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -9 \color{blue}{-14} \\\Leftrightarrow &-15x & = &-23\\\Leftrightarrow & \color{red}{-15}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-23}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{23}{15} } & & \\ & V = \left\{ \frac{23}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{-14}& = & -11 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{-14}\color{blue}{+14-13x } & = & -11 \color{red}{ +13x }\color{blue}{+14-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & -11 \color{blue}{+14} \\\Leftrightarrow &-5x & = &3\\\Leftrightarrow & \color{red}{-5}x & = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{-3}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & -2x \color{red}{-3}\color{blue}{+3-7x } & = & -3 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & -2x \color{blue}{-7x } & = & -3 \color{blue}{+3} \\\Leftrightarrow &-9x & = &0\\\Leftrightarrow & \color{red}{-9}x & = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{+2}& = & 4 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{+2}\color{blue}{-2-4x } & = & 4 \color{red}{ +4x }\color{blue}{-2-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & 4 \color{blue}{-2} \\\Leftrightarrow &11x & = &2\\\Leftrightarrow & \color{red}{11}x & = &2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{+6}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+6}\color{blue}{-6-x } & = & -15 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -15 \color{blue}{-6} \\\Leftrightarrow &-8x & = &-21\\\Leftrightarrow & \color{red}{-8}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-21}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{21}{8} } & & \\ & V = \left\{ \frac{21}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{+1}& = & -11 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+1}\color{blue}{-1+13x } & = & -11 \color{red}{ -13x }\color{blue}{-1+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -11 \color{blue}{-1} \\\Leftrightarrow &20x & = &-12\\\Leftrightarrow & \color{red}{20}x & = &-12\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-12}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{+2}& = & 13 \color{red}{ +8x } \\\Leftrightarrow & 5x \color{red}{+2}\color{blue}{-2-8x } & = & 13 \color{red}{ +8x }\color{blue}{-2-8x } \\\Leftrightarrow & 5x \color{blue}{-8x } & = & 13 \color{blue}{-2} \\\Leftrightarrow &-3x & = &11\\\Leftrightarrow & \color{red}{-3}x & = &11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{-11}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-11}\color{blue}{+11-x } & = & -12 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -12 \color{blue}{+11} \\\Leftrightarrow &13x & = &-1\\\Leftrightarrow & \color{red}{13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{+6}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+6}\color{blue}{-6-x } & = & -8 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -8 \color{blue}{-6} \\\Leftrightarrow &-3x & = &-14\\\Leftrightarrow & \color{red}{-3}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-14}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{14}{3} } & & \\ & V = \left\{ \frac{14}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{-14}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-14}\color{blue}{+14-x } & = & 1 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 1 \color{blue}{+14} \\\Leftrightarrow &7x & = &15\\\Leftrightarrow & \color{red}{7}x & = &15\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{15}{7} \\\Leftrightarrow & \color{green}{ x = \frac{15}{7} } & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{+15}& = & 1 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{+15}\color{blue}{-15-8x } & = & 1 \color{red}{ +8x }\color{blue}{-15-8x } \\\Leftrightarrow & -5x \color{blue}{-8x } & = & 1 \color{blue}{-15} \\\Leftrightarrow &-13x & = &-14\\\Leftrightarrow & \color{red}{-13}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-14}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{14}{13} } & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{+7}& = & 6 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+7}\color{blue}{-7-5x } & = & 6 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 6 \color{blue}{-7} \\\Leftrightarrow &-17x & = &-1\\\Leftrightarrow & \color{red}{-17}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-1}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{1}{17} } & & \\ & V = \left\{ \frac{1}{17} \right\} & \\\end{align}\)