Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{+4}& = & 8 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+4}\color{blue}{-4+11x } & = & 8 \color{red}{ -11x }\color{blue}{-4+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 8 \color{blue}{-4} \\\Leftrightarrow &23x & = &4\\\Leftrightarrow & \color{red}{23}x & = &4\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{4}{23} \\\Leftrightarrow & \color{green}{ x = \frac{4}{23} } & & \\ & V = \left\{ \frac{4}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+6}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+6}\color{blue}{-6-7x } & = & 4 \color{red}{ +7x }\color{blue}{-6-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 4 \color{blue}{-6} \\\Leftrightarrow &3x & = &-2\\\Leftrightarrow & \color{red}{3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-2}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{+15}& = & -10 \color{red}{ +7x } \\\Leftrightarrow & 8x \color{red}{+15}\color{blue}{-15-7x } & = & -10 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & 8x \color{blue}{-7x } & = & -10 \color{blue}{-15} \\\Leftrightarrow &x & = &-25\\\Leftrightarrow & \color{red}{}x & = &-25\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -25 \\\Leftrightarrow & \color{green}{ x = -25 } & & \\ & V = \left\{ -25 \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{+12}& = & -12 \color{red}{ +12x } \\\Leftrightarrow & -7x \color{red}{+12}\color{blue}{-12-12x } & = & -12 \color{red}{ +12x }\color{blue}{-12-12x } \\\Leftrightarrow & -7x \color{blue}{-12x } & = & -12 \color{blue}{-12} \\\Leftrightarrow &-19x & = &-24\\\Leftrightarrow & \color{red}{-19}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-24}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{24}{19} } & & \\ & V = \left\{ \frac{24}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+8}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+8}\color{blue}{-8-x } & = & 14 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 14 \color{blue}{-8} \\\Leftrightarrow &-9x & = &6\\\Leftrightarrow & \color{red}{-9}x & = &6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{-1}& = & 9 \color{red}{ +9x } \\\Leftrightarrow & 10x \color{red}{-1}\color{blue}{+1-9x } & = & 9 \color{red}{ +9x }\color{blue}{+1-9x } \\\Leftrightarrow & 10x \color{blue}{-9x } & = & 9 \color{blue}{+1} \\\Leftrightarrow &x & = &10\\\Leftrightarrow & \color{red}{}x & = &10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 10 \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{-10}& = & 9 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-10}\color{blue}{+10+11x } & = & 9 \color{red}{ -11x }\color{blue}{+10+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 9 \color{blue}{+10} \\\Leftrightarrow &23x & = &19\\\Leftrightarrow & \color{red}{23}x & = &19\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{19}{23} \\\Leftrightarrow & \color{green}{ x = \frac{19}{23} } & & \\ & V = \left\{ \frac{19}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{+11}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+11}\color{blue}{-11-x } & = & 15 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 15 \color{blue}{-11} \\\Leftrightarrow &-7x & = &4\\\Leftrightarrow & \color{red}{-7}x & = &4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+6}& = & -5 \color{red}{ +11x } \\\Leftrightarrow & -x \color{red}{+6}\color{blue}{-6-11x } & = & -5 \color{red}{ +11x }\color{blue}{-6-11x } \\\Leftrightarrow & -x \color{blue}{-11x } & = & -5 \color{blue}{-6} \\\Leftrightarrow &-12x & = &-11\\\Leftrightarrow & \color{red}{-12}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-11}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{11}{12} } & & \\ & V = \left\{ \frac{11}{12} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{-2}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-2}\color{blue}{+2-x } & = & -2 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -2 \color{blue}{+2} \\\Leftrightarrow &-15x & = &0\\\Leftrightarrow & \color{red}{-15}x & = &0\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{0}{-15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{-3}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-3}\color{blue}{+3-x } & = & -12 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -12 \color{blue}{+3} \\\Leftrightarrow &-6x & = &-9\\\Leftrightarrow & \color{red}{-6}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-9}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{+6}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & 14x \color{red}{+6}\color{blue}{-6-13x } & = & -12 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & 14x \color{blue}{-13x } & = & -12 \color{blue}{-6} \\\Leftrightarrow &x & = &-18\\\Leftrightarrow & \color{red}{}x & = &-18\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -18 \\\Leftrightarrow & \color{green}{ x = -18 } & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)