Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{+15}& = & 12 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{+15}\color{blue}{-15+15x } & = & 12 \color{red}{ -15x }\color{blue}{-15+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & 12 \color{blue}{-15} \\\Leftrightarrow &23x & = &-3\\\Leftrightarrow & \color{red}{23}x & = &-3\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-3}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{23} } & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{-6}& = & -1 \color{red}{ +10x } \\\Leftrightarrow & -x \color{red}{-6}\color{blue}{+6-10x } & = & -1 \color{red}{ +10x }\color{blue}{+6-10x } \\\Leftrightarrow & -x \color{blue}{-10x } & = & -1 \color{blue}{+6} \\\Leftrightarrow &-11x & = &5\\\Leftrightarrow & \color{red}{-11}x & = &5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{+3}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+3}\color{blue}{-3-x } & = & 13 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 13 \color{blue}{-3} \\\Leftrightarrow &-6x & = &10\\\Leftrightarrow & \color{red}{-6}x & = &10\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{10}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{+2}& = & -6 \color{red}{ +11x } \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2-11x } & = & -6 \color{red}{ +11x }\color{blue}{-2-11x } \\\Leftrightarrow & 14x \color{blue}{-11x } & = & -6 \color{blue}{-2} \\\Leftrightarrow &3x & = &-8\\\Leftrightarrow & \color{red}{3}x & = &-8\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-8}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{-10}& = & 9 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{-10}\color{blue}{+10-14x } & = & 9 \color{red}{ +14x }\color{blue}{+10-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & 9 \color{blue}{+10} \\\Leftrightarrow &-25x & = &19\\\Leftrightarrow & \color{red}{-25}x & = &19\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{19}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{25} } & & \\ & V = \left\{ \frac{-19}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+9}& = & 4 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{+9}\color{blue}{-9+8x } & = & 4 \color{red}{ -8x }\color{blue}{-9+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & 4 \color{blue}{-9} \\\Leftrightarrow &19x & = &-5\\\Leftrightarrow & \color{red}{19}x & = &-5\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-5}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{19} } & & \\ & V = \left\{ \frac{-5}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{+14}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+14}\color{blue}{-14-x } & = & 7 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 7 \color{blue}{-14} \\\Leftrightarrow &-3x & = &-7\\\Leftrightarrow & \color{red}{-3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{+6}& = & -7 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+6}\color{blue}{-6+3x } & = & -7 \color{red}{ -3x }\color{blue}{-6+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -7 \color{blue}{-6} \\\Leftrightarrow &13x & = &-13\\\Leftrightarrow & \color{red}{13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-13}{13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-6}& = & 15 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-6}\color{blue}{+6+2x } & = & 15 \color{red}{ -2x }\color{blue}{+6+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 15 \color{blue}{+6} \\\Leftrightarrow &17x & = &21\\\Leftrightarrow & \color{red}{17}x & = &21\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{21}{17} \\\Leftrightarrow & \color{green}{ x = \frac{21}{17} } & & \\ & V = \left\{ \frac{21}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{-11}& = & -2 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-11}\color{blue}{+11-5x } & = & -2 \color{red}{ +5x }\color{blue}{+11-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & -2 \color{blue}{+11} \\\Leftrightarrow &x & = &9\\\Leftrightarrow & \color{red}{}x & = &9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 9 \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{-11}& = & 11 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-11}\color{blue}{+11+11x } & = & 11 \color{red}{ -11x }\color{blue}{+11+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & 11 \color{blue}{+11} \\\Leftrightarrow &26x & = &22\\\Leftrightarrow & \color{red}{26}x & = &22\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{22}{26} \\\Leftrightarrow & \color{green}{ x = \frac{11}{13} } & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{-15}& = & 11 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{-15}\color{blue}{+15-11x } & = & 11 \color{red}{ +11x }\color{blue}{+15-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & 11 \color{blue}{+15} \\\Leftrightarrow &-18x & = &26\\\Leftrightarrow & \color{red}{-18}x & = &26\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{26}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{9} } & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)