Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{+15}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15-x } & = & -8 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & -8 \color{blue}{-15} \\\Leftrightarrow &12x & = &-23\\\Leftrightarrow & \color{red}{12}x & = &-23\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-23}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{12} } & & \\ & V = \left\{ \frac{-23}{12} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{-10}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-10}\color{blue}{+10-x } & = & 13 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 13 \color{blue}{+10} \\\Leftrightarrow &-14x & = &23\\\Leftrightarrow & \color{red}{-14}x & = &23\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{23}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{14} } & & \\ & V = \left\{ \frac{-23}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+8}& = & -2 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{+8}\color{blue}{-8-5x } & = & -2 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & 4x \color{blue}{-5x } & = & -2 \color{blue}{-8} \\\Leftrightarrow &-x & = &-10\\\Leftrightarrow & \color{red}{-}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-10}{-1} \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{+10}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+10}\color{blue}{-10-x } & = & 15 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 15 \color{blue}{-10} \\\Leftrightarrow &-4x & = &5\\\Leftrightarrow & \color{red}{-4}x & = &5\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{5}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{+10}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+10}\color{blue}{-10-x } & = & 5 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 5 \color{blue}{-10} \\\Leftrightarrow &-10x & = &-5\\\Leftrightarrow & \color{red}{-10}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-5}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{+2}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+2}\color{blue}{-2-x } & = & -13 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -13 \color{blue}{-2} \\\Leftrightarrow &5x & = &-15\\\Leftrightarrow & \color{red}{5}x & = &-15\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-15}{5} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{+4}& = & -10 \color{red}{ +2x } \\\Leftrightarrow & 11x \color{red}{+4}\color{blue}{-4-2x } & = & -10 \color{red}{ +2x }\color{blue}{-4-2x } \\\Leftrightarrow & 11x \color{blue}{-2x } & = & -10 \color{blue}{-4} \\\Leftrightarrow &9x & = &-14\\\Leftrightarrow & \color{red}{9}x & = &-14\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-14}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{9} } & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{+5}& = & -4 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{+5}\color{blue}{-5+2x } & = & -4 \color{red}{ -2x }\color{blue}{-5+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & -4 \color{blue}{-5} \\\Leftrightarrow &5x & = &-9\\\Leftrightarrow & \color{red}{5}x & = &-9\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-9}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+2}& = & 8 \color{red}{ +8x } \\\Leftrightarrow & -x \color{red}{+2}\color{blue}{-2-8x } & = & 8 \color{red}{ +8x }\color{blue}{-2-8x } \\\Leftrightarrow & -x \color{blue}{-8x } & = & 8 \color{blue}{-2} \\\Leftrightarrow &-9x & = &6\\\Leftrightarrow & \color{red}{-9}x & = &6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{+7}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+7}\color{blue}{-7-7x } & = & 13 \color{red}{ +7x }\color{blue}{-7-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 13 \color{blue}{-7} \\\Leftrightarrow &-17x & = &6\\\Leftrightarrow & \color{red}{-17}x & = &6\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{6}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{17} } & & \\ & V = \left\{ \frac{-6}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-6}& = & 4 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-6}\color{blue}{+6+3x } & = & 4 \color{red}{ -3x }\color{blue}{+6+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 4 \color{blue}{+6} \\\Leftrightarrow &10x & = &10\\\Leftrightarrow & \color{red}{10}x & = &10\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{10}{10} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+14}& = & 13 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14+13x } & = & 13 \color{red}{ -13x }\color{blue}{-14+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & 13 \color{blue}{-14} \\\Leftrightarrow &24x & = &-1\\\Leftrightarrow & \color{red}{24}x & = &-1\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-1}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{24} } & & \\ & V = \left\{ \frac{-1}{24} \right\} & \\\end{align}\)