Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{+6}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+6}\color{blue}{-6-x } & = & -8 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -8 \color{blue}{-6} \\\Leftrightarrow &-8x & = &-14\\\Leftrightarrow & \color{red}{-8}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-14}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{+12}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+12}\color{blue}{-12-x } & = & 6 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 6 \color{blue}{-12} \\\Leftrightarrow &-11x & = &-6\\\Leftrightarrow & \color{red}{-11}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-6}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{+8}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+8}\color{blue}{-8-x } & = & 10 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 10 \color{blue}{-8} \\\Leftrightarrow &-5x & = &2\\\Leftrightarrow & \color{red}{-5}x & = &2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{-15}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-15}\color{blue}{+15-x } & = & -11 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -11 \color{blue}{+15} \\\Leftrightarrow &-3x & = &4\\\Leftrightarrow & \color{red}{-3}x & = &4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{-12}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-12}\color{blue}{+12-x } & = & 5 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 5 \color{blue}{+12} \\\Leftrightarrow &-8x & = &17\\\Leftrightarrow & \color{red}{-8}x & = &17\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{17}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{8} } & & \\ & V = \left\{ \frac{-17}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{-12}& = & -11 \color{red}{ +10x } \\\Leftrightarrow & 13x \color{red}{-12}\color{blue}{+12-10x } & = & -11 \color{red}{ +10x }\color{blue}{+12-10x } \\\Leftrightarrow & 13x \color{blue}{-10x } & = & -11 \color{blue}{+12} \\\Leftrightarrow &3x & = &1\\\Leftrightarrow & \color{red}{3}x & = &1\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{1}{3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{-14}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-14}\color{blue}{+14-x } & = & -5 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -5 \color{blue}{+14} \\\Leftrightarrow &-5x & = &9\\\Leftrightarrow & \color{red}{-5}x & = &9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{+4}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+4}\color{blue}{-4-x } & = & 1 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 1 \color{blue}{-4} \\\Leftrightarrow &13x & = &-3\\\Leftrightarrow & \color{red}{13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-3}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{+8}& = & -11 \color{red}{ -2x } \\\Leftrightarrow & 9x \color{red}{+8}\color{blue}{-8+2x } & = & -11 \color{red}{ -2x }\color{blue}{-8+2x } \\\Leftrightarrow & 9x \color{blue}{+2x } & = & -11 \color{blue}{-8} \\\Leftrightarrow &11x & = &-19\\\Leftrightarrow & \color{red}{11}x & = &-19\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-19}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{11} } & & \\ & V = \left\{ \frac{-19}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-9}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-9}\color{blue}{+9-x } & = & -6 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -6 \color{blue}{+9} \\\Leftrightarrow &9x & = &3\\\Leftrightarrow & \color{red}{9}x & = &3\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{3}{9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{-2}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-2}\color{blue}{+2-x } & = & -7 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -7 \color{blue}{+2} \\\Leftrightarrow &-10x & = &-5\\\Leftrightarrow & \color{red}{-10}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-5}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{-8}& = & 7 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{-8}\color{blue}{+8-14x } & = & 7 \color{red}{ +14x }\color{blue}{+8-14x } \\\Leftrightarrow & 13x \color{blue}{-14x } & = & 7 \color{blue}{+8} \\\Leftrightarrow &-x & = &15\\\Leftrightarrow & \color{red}{-}x & = &15\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{15}{-1} \\\Leftrightarrow & \color{green}{ x = -15 } & & \\ & V = \left\{ -15 \right\} & \\\end{align}\)