Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+8}& = & -15 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{+8}\color{blue}{-8-7x } & = & -15 \color{red}{ +7x }\color{blue}{-8-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & -15 \color{blue}{-8} \\\Leftrightarrow &-4x & = &-23\\\Leftrightarrow & \color{red}{-4}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-23}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{23}{4} } & & \\ & V = \left\{ \frac{23}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{+6}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{+6}\color{blue}{-6-13x } & = & 4 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & 4 \color{blue}{-6} \\\Leftrightarrow &-16x & = &-2\\\Leftrightarrow & \color{red}{-16}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-2}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{+1}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+1}\color{blue}{-1-x } & = & 9 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 9 \color{blue}{-1} \\\Leftrightarrow &-12x & = &8\\\Leftrightarrow & \color{red}{-12}x & = &8\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{8}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{+1}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+1}\color{blue}{-1-x } & = & 13 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 13 \color{blue}{-1} \\\Leftrightarrow &-9x & = &12\\\Leftrightarrow & \color{red}{-9}x & = &12\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{12}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{+1}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+1}\color{blue}{-1-x } & = & -12 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -12 \color{blue}{-1} \\\Leftrightarrow &-11x & = &-13\\\Leftrightarrow & \color{red}{-11}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-13}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{13}{11} } & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{-8}& = & -1 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{-8}\color{blue}{+8-3x } & = & -1 \color{red}{ +3x }\color{blue}{+8-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & -1 \color{blue}{+8} \\\Leftrightarrow &-x & = &7\\\Leftrightarrow & \color{red}{-}x & = &7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{7}{-1} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{-9}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-9}\color{blue}{+9-x } & = & 11 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 11 \color{blue}{+9} \\\Leftrightarrow &-10x & = &20\\\Leftrightarrow & \color{red}{-10}x & = &20\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{20}{-10} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{+12}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12-x } & = & -2 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -2 \color{blue}{-12} \\\Leftrightarrow &-5x & = &-14\\\Leftrightarrow & \color{red}{-5}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-14}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{14}{5} } & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{+2}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{+2}\color{blue}{-2-13x } & = & 13 \color{red}{ +13x }\color{blue}{-2-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & 13 \color{blue}{-2} \\\Leftrightarrow &-3x & = &11\\\Leftrightarrow & \color{red}{-3}x & = &11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+10}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+10}\color{blue}{-10-13x } & = & -1 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -1 \color{blue}{-10} \\\Leftrightarrow &-28x & = &-11\\\Leftrightarrow & \color{red}{-28}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-11}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{11}{28} } & & \\ & V = \left\{ \frac{11}{28} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{+14}& = & -12 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14+2x } & = & -12 \color{red}{ -2x }\color{blue}{-14+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & -12 \color{blue}{-14} \\\Leftrightarrow &13x & = &-26\\\Leftrightarrow & \color{red}{13}x & = &-26\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-26}{13} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+11}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+11}\color{blue}{-11-x } & = & -7 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -7 \color{blue}{-11} \\\Leftrightarrow &-15x & = &-18\\\Leftrightarrow & \color{red}{-15}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-18}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)