Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{-3}& = & 2 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{-3}\color{blue}{+3-10x } & = & 2 \color{red}{ +10x }\color{blue}{+3-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & 2 \color{blue}{+3} \\\Leftrightarrow &-19x & = &5\\\Leftrightarrow & \color{red}{-19}x & = &5\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{5}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{19} } & & \\ & V = \left\{ \frac{-5}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{-4}& = & -8 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-4}\color{blue}{+4+13x } & = & -8 \color{red}{ -13x }\color{blue}{+4+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -8 \color{blue}{+4} \\\Leftrightarrow &24x & = &-4\\\Leftrightarrow & \color{red}{24}x & = &-4\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-4}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{-7}& = & 3 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-7}\color{blue}{+7-7x } & = & 3 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 3 \color{blue}{+7} \\\Leftrightarrow &3x & = &10\\\Leftrightarrow & \color{red}{3}x & = &10\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{10}{3} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{+8}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+8}\color{blue}{-8-x } & = & 10 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 10 \color{blue}{-8} \\\Leftrightarrow &-8x & = &2\\\Leftrightarrow & \color{red}{-8}x & = &2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{-12}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{-12}\color{blue}{+12-7x } & = & 10 \color{red}{ +7x }\color{blue}{+12-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & 10 \color{blue}{+12} \\\Leftrightarrow &2x & = &22\\\Leftrightarrow & \color{red}{2}x & = &22\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{22}{2} \\\Leftrightarrow & \color{green}{ x = 11 } & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+6}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+6}\color{blue}{-6-x } & = & 12 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 12 \color{blue}{-6} \\\Leftrightarrow &-12x & = &6\\\Leftrightarrow & \color{red}{-12}x & = &6\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{6}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{+14}& = & 11 \color{red}{ +9x } \\\Leftrightarrow & 10x \color{red}{+14}\color{blue}{-14-9x } & = & 11 \color{red}{ +9x }\color{blue}{-14-9x } \\\Leftrightarrow & 10x \color{blue}{-9x } & = & 11 \color{blue}{-14} \\\Leftrightarrow &x & = &-3\\\Leftrightarrow & \color{red}{}x & = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{-10}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-10}\color{blue}{+10-x } & = & 15 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 15 \color{blue}{+10} \\\Leftrightarrow &-3x & = &25\\\Leftrightarrow & \color{red}{-3}x & = &25\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{25}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{3} } & & \\ & V = \left\{ \frac{-25}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-11}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & 13x \color{red}{-11}\color{blue}{+11-7x } & = & 10 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & 13x \color{blue}{-7x } & = & 10 \color{blue}{+11} \\\Leftrightarrow &6x & = &21\\\Leftrightarrow & \color{red}{6}x & = &21\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{21}{6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{+2}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+2}\color{blue}{-2-x } & = & -3 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -3 \color{blue}{-2} \\\Leftrightarrow &-3x & = &-5\\\Leftrightarrow & \color{red}{-3}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-5}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{+13}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+13}\color{blue}{-13-x } & = & 4 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 4 \color{blue}{-13} \\\Leftrightarrow &-6x & = &-9\\\Leftrightarrow & \color{red}{-6}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-9}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{+6}& = & -10 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+6}\color{blue}{-6+3x } & = & -10 \color{red}{ -3x }\color{blue}{-6+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -10 \color{blue}{-6} \\\Leftrightarrow &7x & = &-16\\\Leftrightarrow & \color{red}{7}x & = &-16\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-16}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{7} } & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)