Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{+4}& = & -8 \color{red}{ -5x } \\\Leftrightarrow & -x \color{red}{+4}\color{blue}{-4+5x } & = & -8 \color{red}{ -5x }\color{blue}{-4+5x } \\\Leftrightarrow & -x \color{blue}{+5x } & = & -8 \color{blue}{-4} \\\Leftrightarrow &4x & = &-12\\\Leftrightarrow & \color{red}{4}x & = &-12\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-12}{4} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{+4}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+4}\color{blue}{-4-x } & = & 7 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 7 \color{blue}{-4} \\\Leftrightarrow &-13x & = &3\\\Leftrightarrow & \color{red}{-13}x & = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{-15}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-15}\color{blue}{+15-x } & = & 3 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 3 \color{blue}{+15} \\\Leftrightarrow &-5x & = &18\\\Leftrightarrow & \color{red}{-5}x & = &18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{5} } & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{-9}& = & 11 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-9}\color{blue}{+9-11x } & = & 11 \color{red}{ +11x }\color{blue}{+9-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 11 \color{blue}{+9} \\\Leftrightarrow &x & = &20\\\Leftrightarrow & \color{red}{}x & = &20\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 20 \\\Leftrightarrow & \color{green}{ x = 20 } & & \\ & V = \left\{ 20 \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{+11}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+11}\color{blue}{-11-x } & = & -15 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -15 \color{blue}{-11} \\\Leftrightarrow &-10x & = &-26\\\Leftrightarrow & \color{red}{-10}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-26}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{-7}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & 8x \color{red}{-7}\color{blue}{+7-7x } & = & 11 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & 8x \color{blue}{-7x } & = & 11 \color{blue}{+7} \\\Leftrightarrow &x & = &18\\\Leftrightarrow & \color{red}{}x & = &18\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 18 \\\Leftrightarrow & \color{green}{ x = 18 } & & \\ & V = \left\{ 18 \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+4}& = & -7 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+4}\color{blue}{-4-5x } & = & -7 \color{red}{ +5x }\color{blue}{-4-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -7 \color{blue}{-4} \\\Leftrightarrow &-9x & = &-11\\\Leftrightarrow & \color{red}{-9}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{+5}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5-x } & = & 11 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 11 \color{blue}{-5} \\\Leftrightarrow &-4x & = &6\\\Leftrightarrow & \color{red}{-4}x & = &6\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{6}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{-12}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-12}\color{blue}{+12-7x } & = & 2 \color{red}{ +7x }\color{blue}{+12-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 2 \color{blue}{+12} \\\Leftrightarrow &-20x & = &14\\\Leftrightarrow & \color{red}{-20}x & = &14\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{14}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{10} } & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{-4}& = & -1 \color{red}{ -x } \\\Leftrightarrow & x \color{red}{-4}\color{blue}{+4+x } & = & -1 \color{red}{ -x }\color{blue}{+4+x } \\\Leftrightarrow & x \color{blue}{+x } & = & -1 \color{blue}{+4} \\\Leftrightarrow &2x & = &3\\\Leftrightarrow & \color{red}{2}x & = &3\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{3}{2} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{+14}& = & -4 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14+13x } & = & -4 \color{red}{ -13x }\color{blue}{-14+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -4 \color{blue}{-14} \\\Leftrightarrow &24x & = &-18\\\Leftrightarrow & \color{red}{24}x & = &-18\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-18}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{-9}& = & -10 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{-9}\color{blue}{+9-3x } & = & -10 \color{red}{ +3x }\color{blue}{+9-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & -10 \color{blue}{+9} \\\Leftrightarrow &-14x & = &-1\\\Leftrightarrow & \color{red}{-14}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)