Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{-8}& = & 11 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{-8}\color{blue}{+8-3x } & = & 11 \color{red}{ +3x }\color{blue}{+8-3x } \\\Leftrightarrow & 4x \color{blue}{-3x } & = & 11 \color{blue}{+8} \\\Leftrightarrow &x & = &19\\\Leftrightarrow & \color{red}{}x & = &19\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 19 \\\Leftrightarrow & \color{green}{ x = 19 } & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{+9}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -x \color{red}{+9}\color{blue}{-9-x } & = & -7 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -x \color{blue}{-x } & = & -7 \color{blue}{-9} \\\Leftrightarrow &-2x & = &-16\\\Leftrightarrow & \color{red}{-2}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-16}{-2} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{+12}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+12}\color{blue}{-12-x } & = & 2 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 2 \color{blue}{-12} \\\Leftrightarrow &-15x & = &-10\\\Leftrightarrow & \color{red}{-15}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-10}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{-6}& = & 14 \color{red}{ +3x } \\\Leftrightarrow & 14x \color{red}{-6}\color{blue}{+6-3x } & = & 14 \color{red}{ +3x }\color{blue}{+6-3x } \\\Leftrightarrow & 14x \color{blue}{-3x } & = & 14 \color{blue}{+6} \\\Leftrightarrow &11x & = &20\\\Leftrightarrow & \color{red}{11}x & = &20\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{20}{11} \\\Leftrightarrow & \color{green}{ x = \frac{20}{11} } & & \\ & V = \left\{ \frac{20}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+1}& = & -11 \color{red}{ +5x } \\\Leftrightarrow & 9x \color{red}{+1}\color{blue}{-1-5x } & = & -11 \color{red}{ +5x }\color{blue}{-1-5x } \\\Leftrightarrow & 9x \color{blue}{-5x } & = & -11 \color{blue}{-1} \\\Leftrightarrow &4x & = &-12\\\Leftrightarrow & \color{red}{4}x & = &-12\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-12}{4} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{+5}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+5}\color{blue}{-5-x } & = & 1 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 1 \color{blue}{-5} \\\Leftrightarrow &-9x & = &-4\\\Leftrightarrow & \color{red}{-9}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+11}& = & -4 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+11}\color{blue}{-11+11x } & = & -4 \color{red}{ -11x }\color{blue}{-11+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -4 \color{blue}{-11} \\\Leftrightarrow &23x & = &-15\\\Leftrightarrow & \color{red}{23}x & = &-15\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-15}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{23} } & & \\ & V = \left\{ \frac{-15}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{+2}& = & 5 \color{red}{ +3x } \\\Leftrightarrow & 13x \color{red}{+2}\color{blue}{-2-3x } & = & 5 \color{red}{ +3x }\color{blue}{-2-3x } \\\Leftrightarrow & 13x \color{blue}{-3x } & = & 5 \color{blue}{-2} \\\Leftrightarrow &10x & = &3\\\Leftrightarrow & \color{red}{10}x & = &3\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{3}{10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{10} } & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-3}& = & -10 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{-3}\color{blue}{+3-8x } & = & -10 \color{red}{ +8x }\color{blue}{+3-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & -10 \color{blue}{+3} \\\Leftrightarrow &-x & = &-7\\\Leftrightarrow & \color{red}{-}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-7}{-1} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{+15}& = & -11 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+15}\color{blue}{-15-13x } & = & -11 \color{red}{ +13x }\color{blue}{-15-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -11 \color{blue}{-15} \\\Leftrightarrow &-19x & = &-26\\\Leftrightarrow & \color{red}{-19}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-26}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{26}{19} } & & \\ & V = \left\{ \frac{26}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{-14}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-14}\color{blue}{+14-x } & = & 13 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 13 \color{blue}{+14} \\\Leftrightarrow &-14x & = &27\\\Leftrightarrow & \color{red}{-14}x & = &27\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{27}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{14} } & & \\ & V = \left\{ \frac{-27}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{+9}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+9}\color{blue}{-9-x } & = & 10 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 10 \color{blue}{-9} \\\Leftrightarrow &-8x & = &1\\\Leftrightarrow & \color{red}{-8}x & = &1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)