Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{+15}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+15}\color{blue}{-15-x } & = & 15 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 15 \color{blue}{-15} \\\Leftrightarrow &-5x & = &0\\\Leftrightarrow & \color{red}{-5}x & = &0\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{0}{-5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{-14}& = & 8 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{-14}\color{blue}{+14+11x } & = & 8 \color{red}{ -11x }\color{blue}{+14+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & 8 \color{blue}{+14} \\\Leftrightarrow &20x & = &22\\\Leftrightarrow & \color{red}{20}x & = &22\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{22}{20} \\\Leftrightarrow & \color{green}{ x = \frac{11}{10} } & & \\ & V = \left\{ \frac{11}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-2}& = & -6 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-2}\color{blue}{+2-5x } & = & -6 \color{red}{ +5x }\color{blue}{+2-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -6 \color{blue}{+2} \\\Leftrightarrow &7x & = &-4\\\Leftrightarrow & \color{red}{7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{-14}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-14}\color{blue}{+14-x } & = & 11 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 11 \color{blue}{+14} \\\Leftrightarrow &-4x & = &25\\\Leftrightarrow & \color{red}{-4}x & = &25\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{25}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{4} } & & \\ & V = \left\{ \frac{-25}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-6}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-6}\color{blue}{+6-x } & = & -4 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -4 \color{blue}{+6} \\\Leftrightarrow &-6x & = &2\\\Leftrightarrow & \color{red}{-6}x & = &2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{+2}& = & -15 \color{red}{ +4x } \\\Leftrightarrow & x \color{red}{+2}\color{blue}{-2-4x } & = & -15 \color{red}{ +4x }\color{blue}{-2-4x } \\\Leftrightarrow & x \color{blue}{-4x } & = & -15 \color{blue}{-2} \\\Leftrightarrow &-3x & = &-17\\\Leftrightarrow & \color{red}{-3}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-17}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{17}{3} } & & \\ & V = \left\{ \frac{17}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{-14}& = & -6 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-14}\color{blue}{+14-7x } & = & -6 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -6 \color{blue}{+14} \\\Leftrightarrow &-20x & = &8\\\Leftrightarrow & \color{red}{-20}x & = &8\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{8}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{-14}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-14}\color{blue}{+14-x } & = & 2 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 2 \color{blue}{+14} \\\Leftrightarrow &-10x & = &16\\\Leftrightarrow & \color{red}{-10}x & = &16\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{16}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{+2}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+2}\color{blue}{-2-x } & = & 15 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 15 \color{blue}{-2} \\\Leftrightarrow &-5x & = &13\\\Leftrightarrow & \color{red}{-5}x & = &13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{-9}& = & -13 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-9}\color{blue}{+9+3x } & = & -13 \color{red}{ -3x }\color{blue}{+9+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & -13 \color{blue}{+9} \\\Leftrightarrow &10x & = &-4\\\Leftrightarrow & \color{red}{10}x & = &-4\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-4}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{+11}& = & -7 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11+7x } & = & -7 \color{red}{ -7x }\color{blue}{-11+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & -7 \color{blue}{-11} \\\Leftrightarrow &11x & = &-18\\\Leftrightarrow & \color{red}{11}x & = &-18\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-18}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{11} } & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+14}& = & -1 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+14}\color{blue}{-14-11x } & = & -1 \color{red}{ +11x }\color{blue}{-14-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & -1 \color{blue}{-14} \\\Leftrightarrow &-5x & = &-15\\\Leftrightarrow & \color{red}{-5}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-15}{-5} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)