Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{+1}& = & -4 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{+1}\color{blue}{-1-4x } & = & -4 \color{red}{ +4x }\color{blue}{-1-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & -4 \color{blue}{-1} \\\Leftrightarrow &-7x & = &-5\\\Leftrightarrow & \color{red}{-7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{-12}& = & 15 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12-8x } & = & 15 \color{red}{ +8x }\color{blue}{+12-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & 15 \color{blue}{+12} \\\Leftrightarrow &-23x & = &27\\\Leftrightarrow & \color{red}{-23}x & = &27\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{27}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{23} } & & \\ & V = \left\{ \frac{-27}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{+2}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{+2}\color{blue}{-2-13x } & = & 5 \color{red}{ +13x }\color{blue}{-2-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & 5 \color{blue}{-2} \\\Leftrightarrow &-17x & = &3\\\Leftrightarrow & \color{red}{-17}x & = &3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{17} } & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{+2}& = & 15 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+2}\color{blue}{-2+7x } & = & 15 \color{red}{ -7x }\color{blue}{-2+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 15 \color{blue}{-2} \\\Leftrightarrow &15x & = &13\\\Leftrightarrow & \color{red}{15}x & = &13\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{13}{15} \\\Leftrightarrow & \color{green}{ x = \frac{13}{15} } & & \\ & V = \left\{ \frac{13}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{+12}& = & -7 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12-5x } & = & -7 \color{red}{ +5x }\color{blue}{-12-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -7 \color{blue}{-12} \\\Leftrightarrow &-9x & = &-19\\\Leftrightarrow & \color{red}{-9}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-19}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{19}{9} } & & \\ & V = \left\{ \frac{19}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{+10}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+10}\color{blue}{-10-x } & = & -3 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -3 \color{blue}{-10} \\\Leftrightarrow &-4x & = &-13\\\Leftrightarrow & \color{red}{-4}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-13}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{13}{4} } & & \\ & V = \left\{ \frac{13}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{-12}& = & 1 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{-12}\color{blue}{+12-5x } & = & 1 \color{red}{ +5x }\color{blue}{+12-5x } \\\Leftrightarrow & 4x \color{blue}{-5x } & = & 1 \color{blue}{+12} \\\Leftrightarrow &-x & = &13\\\Leftrightarrow & \color{red}{-}x & = &13\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{13}{-1} \\\Leftrightarrow & \color{green}{ x = -13 } & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-2}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{-2}\color{blue}{+2-x } & = & -8 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -8 \color{blue}{+2} \\\Leftrightarrow &8x & = &-6\\\Leftrightarrow & \color{red}{8}x & = &-6\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-6}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+12}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+12}\color{blue}{-12-x } & = & -11 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -11 \color{blue}{-12} \\\Leftrightarrow &-7x & = &-23\\\Leftrightarrow & \color{red}{-7}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-23}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{23}{7} } & & \\ & V = \left\{ \frac{23}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{-1}& = & 11 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-1}\color{blue}{+1+11x } & = & 11 \color{red}{ -11x }\color{blue}{+1+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 11 \color{blue}{+1} \\\Leftrightarrow &17x & = &12\\\Leftrightarrow & \color{red}{17}x & = &12\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{12}{17} \\\Leftrightarrow & \color{green}{ x = \frac{12}{17} } & & \\ & V = \left\{ \frac{12}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-13}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-13}\color{blue}{+13-x } & = & -1 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -1 \color{blue}{+13} \\\Leftrightarrow &-15x & = &12\\\Leftrightarrow & \color{red}{-15}x & = &12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{-10}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-10}\color{blue}{+10-x } & = & 1 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 1 \color{blue}{+10} \\\Leftrightarrow &-12x & = &11\\\Leftrightarrow & \color{red}{-12}x & = &11\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{11}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{12} } & & \\ & V = \left\{ \frac{-11}{12} \right\} & \\\end{align}\)