Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{+10}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+10}\color{blue}{-10-x } & = & -2 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -2 \color{blue}{-10} \\\Leftrightarrow &-15x & = &-12\\\Leftrightarrow & \color{red}{-15}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{+14}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+14}\color{blue}{-14-x } & = & -2 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -2 \color{blue}{-14} \\\Leftrightarrow &-12x & = &-16\\\Leftrightarrow & \color{red}{-12}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-16}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-8}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-8}\color{blue}{+8-x } & = & 12 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 12 \color{blue}{+8} \\\Leftrightarrow &11x & = &20\\\Leftrightarrow & \color{red}{11}x & = &20\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{20}{11} \\\Leftrightarrow & \color{green}{ x = \frac{20}{11} } & & \\ & V = \left\{ \frac{20}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{+14}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+14}\color{blue}{-14-x } & = & -7 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -7 \color{blue}{-14} \\\Leftrightarrow &-12x & = &-21\\\Leftrightarrow & \color{red}{-12}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-21}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{+2}& = & -9 \color{red}{ +8x } \\\Leftrightarrow & 3x \color{red}{+2}\color{blue}{-2-8x } & = & -9 \color{red}{ +8x }\color{blue}{-2-8x } \\\Leftrightarrow & 3x \color{blue}{-8x } & = & -9 \color{blue}{-2} \\\Leftrightarrow &-5x & = &-11\\\Leftrightarrow & \color{red}{-5}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-11}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-11}\color{blue}{+11-x } & = & 14 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 14 \color{blue}{+11} \\\Leftrightarrow &-14x & = &25\\\Leftrightarrow & \color{red}{-14}x & = &25\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{25}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{14} } & & \\ & V = \left\{ \frac{-25}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{+11}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+11}\color{blue}{-11-x } & = & 10 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 10 \color{blue}{-11} \\\Leftrightarrow &-15x & = &-1\\\Leftrightarrow & \color{red}{-15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+2}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+2}\color{blue}{-2-x } & = & 12 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 12 \color{blue}{-2} \\\Leftrightarrow &x & = &10\\\Leftrightarrow & \color{red}{}x & = &10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 10 \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{-15}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-15}\color{blue}{+15-x } & = & 7 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 7 \color{blue}{+15} \\\Leftrightarrow &-12x & = &22\\\Leftrightarrow & \color{red}{-12}x & = &22\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{22}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{6} } & & \\ & V = \left\{ \frac{-11}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-4}& = & 2 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{-4}\color{blue}{+4-5x } & = & 2 \color{red}{ +5x }\color{blue}{+4-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 2 \color{blue}{+4} \\\Leftrightarrow &-17x & = &6\\\Leftrightarrow & \color{red}{-17}x & = &6\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{6}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{17} } & & \\ & V = \left\{ \frac{-6}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{-6}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-6}\color{blue}{+6-7x } & = & 11 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 11 \color{blue}{+6} \\\Leftrightarrow &-17x & = &17\\\Leftrightarrow & \color{red}{-17}x & = &17\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{17}{-17} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{-4}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-4}\color{blue}{+4-x } & = & 5 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 5 \color{blue}{+4} \\\Leftrightarrow &-5x & = &9\\\Leftrightarrow & \color{red}{-5}x & = &9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)