Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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