Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+7}& = & 13 \color{red}{ +2x } \\\Leftrightarrow & -13x \color{red}{+7}\color{blue}{-7-2x } & = & 13 \color{red}{ +2x }\color{blue}{-7-2x } \\\Leftrightarrow & -13x \color{blue}{-2x } & = & 13 \color{blue}{-7} \\\Leftrightarrow &-15x & = &6\\\Leftrightarrow & \color{red}{-15}x & = &6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{-2}& = & -15 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{-2}\color{blue}{+2-6x } & = & -15 \color{red}{ +6x }\color{blue}{+2-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & -15 \color{blue}{+2} \\\Leftrightarrow &-x & = &-13\\\Leftrightarrow & \color{red}{-}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-13}{-1} \\\Leftrightarrow & \color{green}{ x = 13 } & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{-14}& = & -7 \color{red}{ -3x } \\\Leftrightarrow & -x \color{red}{-14}\color{blue}{+14+3x } & = & -7 \color{red}{ -3x }\color{blue}{+14+3x } \\\Leftrightarrow & -x \color{blue}{+3x } & = & -7 \color{blue}{+14} \\\Leftrightarrow &2x & = &7\\\Leftrightarrow & \color{red}{2}x & = &7\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{7}{2} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+2}& = & 6 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+2}\color{blue}{-2+5x } & = & 6 \color{red}{ -5x }\color{blue}{-2+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 6 \color{blue}{-2} \\\Leftrightarrow &11x & = &4\\\Leftrightarrow & \color{red}{11}x & = &4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+4}& = & -1 \color{red}{ -15x } \\\Leftrightarrow & -8x \color{red}{+4}\color{blue}{-4+15x } & = & -1 \color{red}{ -15x }\color{blue}{-4+15x } \\\Leftrightarrow & -8x \color{blue}{+15x } & = & -1 \color{blue}{-4} \\\Leftrightarrow &7x & = &-5\\\Leftrightarrow & \color{red}{7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-5}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{+10}& = & 7 \color{red}{ -11x } \\\Leftrightarrow & -x \color{red}{+10}\color{blue}{-10+11x } & = & 7 \color{red}{ -11x }\color{blue}{-10+11x } \\\Leftrightarrow & -x \color{blue}{+11x } & = & 7 \color{blue}{-10} \\\Leftrightarrow &10x & = &-3\\\Leftrightarrow & \color{red}{10}x & = &-3\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-3}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{-11}& = & 6 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{-11}\color{blue}{+11-13x } & = & 6 \color{red}{ +13x }\color{blue}{+11-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & 6 \color{blue}{+11} \\\Leftrightarrow &-x & = &17\\\Leftrightarrow & \color{red}{-}x & = &17\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{17}{-1} \\\Leftrightarrow & \color{green}{ x = -17 } & & \\ & V = \left\{ -17 \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{+11}& = & -13 \color{red}{ +11x } \\\Leftrightarrow & 14x \color{red}{+11}\color{blue}{-11-11x } & = & -13 \color{red}{ +11x }\color{blue}{-11-11x } \\\Leftrightarrow & 14x \color{blue}{-11x } & = & -13 \color{blue}{-11} \\\Leftrightarrow &3x & = &-24\\\Leftrightarrow & \color{red}{3}x & = &-24\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-24}{3} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{+4}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & 14x \color{red}{+4}\color{blue}{-4-11x } & = & -3 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & 14x \color{blue}{-11x } & = & -3 \color{blue}{-4} \\\Leftrightarrow &3x & = &-7\\\Leftrightarrow & \color{red}{3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-7}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{+7}& = & -12 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+7}\color{blue}{-7+9x } & = & -12 \color{red}{ -9x }\color{blue}{-7+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & -12 \color{blue}{-7} \\\Leftrightarrow &19x & = &-19\\\Leftrightarrow & \color{red}{19}x & = &-19\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-19}{19} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{+7}& = & 7 \color{red}{ -11x } \\\Leftrightarrow & -14x \color{red}{+7}\color{blue}{-7+11x } & = & 7 \color{red}{ -11x }\color{blue}{-7+11x } \\\Leftrightarrow & -14x \color{blue}{+11x } & = & 7 \color{blue}{-7} \\\Leftrightarrow &-3x & = &0\\\Leftrightarrow & \color{red}{-3}x & = &0\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{0}{-3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{-2}& = & 11 \color{red}{ +4x } \\\Leftrightarrow & 5x \color{red}{-2}\color{blue}{+2-4x } & = & 11 \color{red}{ +4x }\color{blue}{+2-4x } \\\Leftrightarrow & 5x \color{blue}{-4x } & = & 11 \color{blue}{+2} \\\Leftrightarrow &x & = &13\\\Leftrightarrow & \color{red}{}x & = &13\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 13 \\\Leftrightarrow & \color{green}{ x = 13 } & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)