Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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