Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{-14}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-14}\color{blue}{+14-x } & = & 7 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 7 \color{blue}{+14} \\\Leftrightarrow &-9x & = &21\\\Leftrightarrow & \color{red}{-9}x & = &21\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{21}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{-4}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{-4}\color{blue}{+4-13x } & = & 13 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & 13 \color{blue}{+4} \\\Leftrightarrow &-3x & = &17\\\Leftrightarrow & \color{red}{-3}x & = &17\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{17}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{3} } & & \\ & V = \left\{ \frac{-17}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+4}& = & -6 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{+4}\color{blue}{-4-11x } & = & -6 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & -6 \color{blue}{-4} \\\Leftrightarrow &4x & = &-10\\\Leftrightarrow & \color{red}{4}x & = &-10\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-10}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{-8}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-8}\color{blue}{+8-x } & = & 3 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 3 \color{blue}{+8} \\\Leftrightarrow &-14x & = &11\\\Leftrightarrow & \color{red}{-14}x & = &11\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{11}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{14} } & & \\ & V = \left\{ \frac{-11}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{-12}& = & 5 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{-12}\color{blue}{+12+15x } & = & 5 \color{red}{ -15x }\color{blue}{+12+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & 5 \color{blue}{+12} \\\Leftrightarrow &23x & = &17\\\Leftrightarrow & \color{red}{23}x & = &17\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{17}{23} \\\Leftrightarrow & \color{green}{ x = \frac{17}{23} } & & \\ & V = \left\{ \frac{17}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+12}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+12}\color{blue}{-12-x } & = & 11 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &-11x & = &-1\\\Leftrightarrow & \color{red}{-11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+15}& = & -3 \color{red}{ -9x } \\\Leftrightarrow & 7x \color{red}{+15}\color{blue}{-15+9x } & = & -3 \color{red}{ -9x }\color{blue}{-15+9x } \\\Leftrightarrow & 7x \color{blue}{+9x } & = & -3 \color{blue}{-15} \\\Leftrightarrow &16x & = &-18\\\Leftrightarrow & \color{red}{16}x & = &-18\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-18}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{+9}& = & 2 \color{red}{ +8x } \\\Leftrightarrow & 13x \color{red}{+9}\color{blue}{-9-8x } & = & 2 \color{red}{ +8x }\color{blue}{-9-8x } \\\Leftrightarrow & 13x \color{blue}{-8x } & = & 2 \color{blue}{-9} \\\Leftrightarrow &5x & = &-7\\\Leftrightarrow & \color{red}{5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-7}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{-10}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-10}\color{blue}{+10-x } & = & -9 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -9 \color{blue}{+10} \\\Leftrightarrow &-6x & = &1\\\Leftrightarrow & \color{red}{-6}x & = &1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+4}& = & 14 \color{red}{ +5x } \\\Leftrightarrow & 7x \color{red}{+4}\color{blue}{-4-5x } & = & 14 \color{red}{ +5x }\color{blue}{-4-5x } \\\Leftrightarrow & 7x \color{blue}{-5x } & = & 14 \color{blue}{-4} \\\Leftrightarrow &2x & = &10\\\Leftrightarrow & \color{red}{2}x & = &10\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{10}{2} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{-9}& = & 5 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{-9}\color{blue}{+9-12x } & = & 5 \color{red}{ +12x }\color{blue}{+9-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & 5 \color{blue}{+9} \\\Leftrightarrow &-23x & = &14\\\Leftrightarrow & \color{red}{-23}x & = &14\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{14}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{23} } & & \\ & V = \left\{ \frac{-14}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{-9}& = & -8 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-9}\color{blue}{+9-11x } & = & -8 \color{red}{ +11x }\color{blue}{+9-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -8 \color{blue}{+9} \\\Leftrightarrow &x & = &1\\\Leftrightarrow & \color{red}{}x & = &1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 1 \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)