Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{-15}& = & 11 \color{red}{ -3x } \\\Leftrightarrow & -x \color{red}{-15}\color{blue}{+15+3x } & = & 11 \color{red}{ -3x }\color{blue}{+15+3x } \\\Leftrightarrow & -x \color{blue}{+3x } & = & 11 \color{blue}{+15} \\\Leftrightarrow &2x & = &26\\\Leftrightarrow & \color{red}{2}x & = &26\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{26}{2} \\\Leftrightarrow & \color{green}{ x = 13 } & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-4}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & 3x \color{red}{-4}\color{blue}{+4-11x } & = & -3 \color{red}{ +11x }\color{blue}{+4-11x } \\\Leftrightarrow & 3x \color{blue}{-11x } & = & -3 \color{blue}{+4} \\\Leftrightarrow &-8x & = &1\\\Leftrightarrow & \color{red}{-8}x & = &1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{-2}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-2}\color{blue}{+2-x } & = & -5 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -5 \color{blue}{+2} \\\Leftrightarrow &3x & = &-3\\\Leftrightarrow & \color{red}{3}x & = &-3\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-3}{3} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{-7}& = & -3 \color{red}{ +10x } \\\Leftrightarrow & -11x \color{red}{-7}\color{blue}{+7-10x } & = & -3 \color{red}{ +10x }\color{blue}{+7-10x } \\\Leftrightarrow & -11x \color{blue}{-10x } & = & -3 \color{blue}{+7} \\\Leftrightarrow &-21x & = &4\\\Leftrightarrow & \color{red}{-21}x & = &4\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{4}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{21} } & & \\ & V = \left\{ \frac{-4}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{+15}& = & 11 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{+15}\color{blue}{-15-5x } & = & 11 \color{red}{ +5x }\color{blue}{-15-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & 11 \color{blue}{-15} \\\Leftrightarrow &-19x & = &-4\\\Leftrightarrow & \color{red}{-19}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-4}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{4}{19} } & & \\ & V = \left\{ \frac{4}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-7}& = & 2 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{-7}\color{blue}{+7+10x } & = & 2 \color{red}{ -10x }\color{blue}{+7+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & 2 \color{blue}{+7} \\\Leftrightarrow &17x & = &9\\\Leftrightarrow & \color{red}{17}x & = &9\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{9}{17} \\\Leftrightarrow & \color{green}{ x = \frac{9}{17} } & & \\ & V = \left\{ \frac{9}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{-9}& = & 2 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{-9}\color{blue}{+9-5x } & = & 2 \color{red}{ +5x }\color{blue}{+9-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & 2 \color{blue}{+9} \\\Leftrightarrow &-19x & = &11\\\Leftrightarrow & \color{red}{-19}x & = &11\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{11}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{19} } & & \\ & V = \left\{ \frac{-11}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{+5}& = & 8 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{+5}\color{blue}{-5-13x } & = & 8 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & 4x \color{blue}{-13x } & = & 8 \color{blue}{-5} \\\Leftrightarrow &-9x & = &3\\\Leftrightarrow & \color{red}{-9}x & = &3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{-10}& = & 10 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{-10}\color{blue}{+10-3x } & = & 10 \color{red}{ +3x }\color{blue}{+10-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & 10 \color{blue}{+10} \\\Leftrightarrow &-8x & = &20\\\Leftrightarrow & \color{red}{-8}x & = &20\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{20}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-5}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5-x } & = & 14 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 14 \color{blue}{+5} \\\Leftrightarrow &-9x & = &19\\\Leftrightarrow & \color{red}{-9}x & = &19\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{19}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{9} } & & \\ & V = \left\{ \frac{-19}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{-11}& = & 10 \color{red}{ -4x } \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11+4x } & = & 10 \color{red}{ -4x }\color{blue}{+11+4x } \\\Leftrightarrow & -5x \color{blue}{+4x } & = & 10 \color{blue}{+11} \\\Leftrightarrow &-x & = &21\\\Leftrightarrow & \color{red}{-}x & = &21\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{21}{-1} \\\Leftrightarrow & \color{green}{ x = -21 } & & \\ & V = \left\{ -21 \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{+4}& = & 3 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+4}\color{blue}{-4+7x } & = & 3 \color{red}{ -7x }\color{blue}{-4+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 3 \color{blue}{-4} \\\Leftrightarrow &15x & = &-1\\\Leftrightarrow & \color{red}{15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-1}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{15} } & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)