Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{+15}& = & -14 \color{red}{ -2x } \\\Leftrightarrow & -x \color{red}{+15}\color{blue}{-15+2x } & = & -14 \color{red}{ -2x }\color{blue}{-15+2x } \\\Leftrightarrow & -x \color{blue}{+2x } & = & -14 \color{blue}{-15} \\\Leftrightarrow &x & = &-29\\\Leftrightarrow & \color{red}{}x & = &-29\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -29 \\\Leftrightarrow & \color{green}{ x = -29 } & & \\ & V = \left\{ -29 \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{-3}& = & 5 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-3}\color{blue}{+3-11x } & = & 5 \color{red}{ +11x }\color{blue}{+3-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & 5 \color{blue}{+3} \\\Leftrightarrow &-21x & = &8\\\Leftrightarrow & \color{red}{-21}x & = &8\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{8}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{21} } & & \\ & V = \left\{ \frac{-8}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-7}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{-7}\color{blue}{+7-x } & = & 12 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & 12 \color{blue}{+7} \\\Leftrightarrow &10x & = &19\\\Leftrightarrow & \color{red}{10}x & = &19\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{19}{10} \\\Leftrightarrow & \color{green}{ x = \frac{19}{10} } & & \\ & V = \left\{ \frac{19}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{+15}& = & 5 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{+15}\color{blue}{-15-11x } & = & 5 \color{red}{ +11x }\color{blue}{-15-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & 5 \color{blue}{-15} \\\Leftrightarrow &-3x & = &-10\\\Leftrightarrow & \color{red}{-3}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-10}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{+9}& = & -9 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+9}\color{blue}{-9-7x } & = & -9 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -9 \color{blue}{-9} \\\Leftrightarrow &3x & = &-18\\\Leftrightarrow & \color{red}{3}x & = &-18\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-18}{3} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{+4}& = & -8 \color{red}{ +3x } \\\Leftrightarrow & 13x \color{red}{+4}\color{blue}{-4-3x } & = & -8 \color{red}{ +3x }\color{blue}{-4-3x } \\\Leftrightarrow & 13x \color{blue}{-3x } & = & -8 \color{blue}{-4} \\\Leftrightarrow &10x & = &-12\\\Leftrightarrow & \color{red}{10}x & = &-12\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-12}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{-2}& = & -11 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{-2}\color{blue}{+2-3x } & = & -11 \color{red}{ +3x }\color{blue}{+2-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & -11 \color{blue}{+2} \\\Leftrightarrow &-8x & = &-9\\\Leftrightarrow & \color{red}{-8}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-9}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{-7}& = & 8 \color{red}{ +11x } \\\Leftrightarrow & 7x \color{red}{-7}\color{blue}{+7-11x } & = & 8 \color{red}{ +11x }\color{blue}{+7-11x } \\\Leftrightarrow & 7x \color{blue}{-11x } & = & 8 \color{blue}{+7} \\\Leftrightarrow &-4x & = &15\\\Leftrightarrow & \color{red}{-4}x & = &15\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{15}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{4} } & & \\ & V = \left\{ \frac{-15}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{-14}& = & 12 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{-14}\color{blue}{+14+5x } & = & 12 \color{red}{ -5x }\color{blue}{+14+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & 12 \color{blue}{+14} \\\Leftrightarrow &16x & = &26\\\Leftrightarrow & \color{red}{16}x & = &26\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{26}{16} \\\Leftrightarrow & \color{green}{ x = \frac{13}{8} } & & \\ & V = \left\{ \frac{13}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{-9}& = & 5 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-9}\color{blue}{+9+5x } & = & 5 \color{red}{ -5x }\color{blue}{+9+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & 5 \color{blue}{+9} \\\Leftrightarrow &8x & = &14\\\Leftrightarrow & \color{red}{8}x & = &14\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{14}{8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{-4}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{-4}\color{blue}{+4-x } & = & -6 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & -6 \color{blue}{+4} \\\Leftrightarrow &4x & = &-2\\\Leftrightarrow & \color{red}{4}x & = &-2\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-2}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+10}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+10}\color{blue}{-10-x } & = & -9 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -9 \color{blue}{-10} \\\Leftrightarrow &-10x & = &-19\\\Leftrightarrow & \color{red}{-10}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-19}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{19}{10} } & & \\ & V = \left\{ \frac{19}{10} \right\} & \\\end{align}\)