Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{-15}& = & 10 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{-15}\color{blue}{+15-11x } & = & 10 \color{red}{ +11x }\color{blue}{+15-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & 10 \color{blue}{+15} \\\Leftrightarrow &-3x & = &25\\\Leftrightarrow & \color{red}{-3}x & = &25\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{25}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{3} } & & \\ & V = \left\{ \frac{-25}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+6}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+6}\color{blue}{-6-x } & = & -9 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -9 \color{blue}{-6} \\\Leftrightarrow &-3x & = &-15\\\Leftrightarrow & \color{red}{-3}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-15}{-3} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{+6}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6-x } & = & 10 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 10 \color{blue}{-6} \\\Leftrightarrow &-10x & = &4\\\Leftrightarrow & \color{red}{-10}x & = &4\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{4}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{-8}& = & 15 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8+9x } & = & 15 \color{red}{ -9x }\color{blue}{+8+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & 15 \color{blue}{+8} \\\Leftrightarrow &19x & = &23\\\Leftrightarrow & \color{red}{19}x & = &23\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{23}{19} \\\Leftrightarrow & \color{green}{ x = \frac{23}{19} } & & \\ & V = \left\{ \frac{23}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{+10}& = & 1 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{+10}\color{blue}{-10-4x } & = & 1 \color{red}{ +4x }\color{blue}{-10-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & 1 \color{blue}{-10} \\\Leftrightarrow &11x & = &-9\\\Leftrightarrow & \color{red}{11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{+3}& = & 3 \color{red}{ -10x } \\\Leftrightarrow & -x \color{red}{+3}\color{blue}{-3+10x } & = & 3 \color{red}{ -10x }\color{blue}{-3+10x } \\\Leftrightarrow & -x \color{blue}{+10x } & = & 3 \color{blue}{-3} \\\Leftrightarrow &9x & = &0\\\Leftrightarrow & \color{red}{9}x & = &0\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{0}{9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{-1}& = & -3 \color{red}{ +6x } \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1-6x } & = & -3 \color{red}{ +6x }\color{blue}{+1-6x } \\\Leftrightarrow & -x \color{blue}{-6x } & = & -3 \color{blue}{+1} \\\Leftrightarrow &-7x & = &-2\\\Leftrightarrow & \color{red}{-7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+6}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+6}\color{blue}{-6-x } & = & 11 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 11 \color{blue}{-6} \\\Leftrightarrow &-12x & = &5\\\Leftrightarrow & \color{red}{-12}x & = &5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{12} } & & \\ & V = \left\{ \frac{-5}{12} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+4}& = & -13 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+4}\color{blue}{-4+6x } & = & -13 \color{red}{ -6x }\color{blue}{-4+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -13 \color{blue}{-4} \\\Leftrightarrow &19x & = &-17\\\Leftrightarrow & \color{red}{19}x & = &-17\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-17}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{19} } & & \\ & V = \left\{ \frac{-17}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{-14}& = & 3 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-14}\color{blue}{+14-6x } & = & 3 \color{red}{ +6x }\color{blue}{+14-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & 3 \color{blue}{+14} \\\Leftrightarrow &-11x & = &17\\\Leftrightarrow & \color{red}{-11}x & = &17\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{17}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{11} } & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{-15}& = & -14 \color{red}{ +3x } \\\Leftrightarrow & 10x \color{red}{-15}\color{blue}{+15-3x } & = & -14 \color{red}{ +3x }\color{blue}{+15-3x } \\\Leftrightarrow & 10x \color{blue}{-3x } & = & -14 \color{blue}{+15} \\\Leftrightarrow &7x & = &1\\\Leftrightarrow & \color{red}{7}x & = &1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{+10}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+10}\color{blue}{-10-13x } & = & 2 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 2 \color{blue}{-10} \\\Leftrightarrow &-19x & = &-8\\\Leftrightarrow & \color{red}{-19}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-8}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{8}{19} } & & \\ & V = \left\{ \frac{8}{19} \right\} & \\\end{align}\)