Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{-10}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10-x } & = & 6 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 6 \color{blue}{+10} \\\Leftrightarrow &-11x & = &16\\\Leftrightarrow & \color{red}{-11}x & = &16\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{16}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{11} } & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+5}& = & -4 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+5}\color{blue}{-5+13x } & = & -4 \color{red}{ -13x }\color{blue}{-5+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -4 \color{blue}{-5} \\\Leftrightarrow &27x & = &-9\\\Leftrightarrow & \color{red}{27}x & = &-9\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-9}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{-8}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-8}\color{blue}{+8-x } & = & 1 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 1 \color{blue}{+8} \\\Leftrightarrow &7x & = &9\\\Leftrightarrow & \color{red}{7}x & = &9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{+11}& = & 15 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+11}\color{blue}{-11+13x } & = & 15 \color{red}{ -13x }\color{blue}{-11+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 15 \color{blue}{-11} \\\Leftrightarrow &27x & = &4\\\Leftrightarrow & \color{red}{27}x & = &4\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{4}{27} \\\Leftrightarrow & \color{green}{ x = \frac{4}{27} } & & \\ & V = \left\{ \frac{4}{27} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{-2}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-2}\color{blue}{+2-x } & = & -6 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -6 \color{blue}{+2} \\\Leftrightarrow &-10x & = &-4\\\Leftrightarrow & \color{red}{-10}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-4}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{+5}& = & -9 \color{red}{ +2x } \\\Leftrightarrow & 5x \color{red}{+5}\color{blue}{-5-2x } & = & -9 \color{red}{ +2x }\color{blue}{-5-2x } \\\Leftrightarrow & 5x \color{blue}{-2x } & = & -9 \color{blue}{-5} \\\Leftrightarrow &3x & = &-14\\\Leftrightarrow & \color{red}{3}x & = &-14\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-14}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{3} } & & \\ & V = \left\{ \frac{-14}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{-14}& = & 8 \color{red}{ -7x } \\\Leftrightarrow & 11x \color{red}{-14}\color{blue}{+14+7x } & = & 8 \color{red}{ -7x }\color{blue}{+14+7x } \\\Leftrightarrow & 11x \color{blue}{+7x } & = & 8 \color{blue}{+14} \\\Leftrightarrow &18x & = &22\\\Leftrightarrow & \color{red}{18}x & = &22\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{22}{18} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{-5}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-5}\color{blue}{+5-x } & = & 3 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 3 \color{blue}{+5} \\\Leftrightarrow &-16x & = &8\\\Leftrightarrow & \color{red}{-16}x & = &8\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{8}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{-4}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-4}\color{blue}{+4-x } & = & 14 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 14 \color{blue}{+4} \\\Leftrightarrow &-4x & = &18\\\Leftrightarrow & \color{red}{-4}x & = &18\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{18}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{2} } & & \\ & V = \left\{ \frac{-9}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{-7}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-7}\color{blue}{+7-x } & = & 10 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 10 \color{blue}{+7} \\\Leftrightarrow &-16x & = &17\\\Leftrightarrow & \color{red}{-16}x & = &17\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{17}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{16} } & & \\ & V = \left\{ \frac{-17}{16} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{+9}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+9}\color{blue}{-9-x } & = & 1 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 1 \color{blue}{-9} \\\Leftrightarrow &-8x & = &-8\\\Leftrightarrow & \color{red}{-8}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-8}{-8} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{-2}& = & 10 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{-2}\color{blue}{+2+15x } & = & 10 \color{red}{ -15x }\color{blue}{+2+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & 10 \color{blue}{+2} \\\Leftrightarrow &19x & = &12\\\Leftrightarrow & \color{red}{19}x & = &12\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{12}{19} \\\Leftrightarrow & \color{green}{ x = \frac{12}{19} } & & \\ & V = \left\{ \frac{12}{19} \right\} & \\\end{align}\)