Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{-15}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-15}\color{blue}{+15-x } & = & 6 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 6 \color{blue}{+15} \\\Leftrightarrow &-8x & = &21\\\Leftrightarrow & \color{red}{-8}x & = &21\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{21}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{8} } & & \\ & V = \left\{ \frac{-21}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{+3}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+3}\color{blue}{-3-x } & = & 2 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 2 \color{blue}{-3} \\\Leftrightarrow &-10x & = &-1\\\Leftrightarrow & \color{red}{-10}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-10}& = & -12 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-10}\color{blue}{+10+13x } & = & -12 \color{red}{ -13x }\color{blue}{+10+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -12 \color{blue}{+10} \\\Leftrightarrow &24x & = &-2\\\Leftrightarrow & \color{red}{24}x & = &-2\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-2}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{12} } & & \\ & V = \left\{ \frac{-1}{12} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{-1}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{-1}\color{blue}{+1-x } & = & 1 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & 1 \color{blue}{+1} \\\Leftrightarrow &8x & = &2\\\Leftrightarrow & \color{red}{8}x & = &2\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{2}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{+12}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+12}\color{blue}{-12-x } & = & -3 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -3 \color{blue}{-12} \\\Leftrightarrow &-3x & = &-15\\\Leftrightarrow & \color{red}{-3}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-15}{-3} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{-8}& = & -2 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8+9x } & = & -2 \color{red}{ -9x }\color{blue}{+8+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & -2 \color{blue}{+8} \\\Leftrightarrow &19x & = &6\\\Leftrightarrow & \color{red}{19}x & = &6\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{6}{19} \\\Leftrightarrow & \color{green}{ x = \frac{6}{19} } & & \\ & V = \left\{ \frac{6}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{+15}& = & 5 \color{red}{ +8x } \\\Leftrightarrow & -x \color{red}{+15}\color{blue}{-15-8x } & = & 5 \color{red}{ +8x }\color{blue}{-15-8x } \\\Leftrightarrow & -x \color{blue}{-8x } & = & 5 \color{blue}{-15} \\\Leftrightarrow &-9x & = &-10\\\Leftrightarrow & \color{red}{-9}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{10}{9} } & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{-12}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & 14x \color{red}{-12}\color{blue}{+12-11x } & = & 3 \color{red}{ +11x }\color{blue}{+12-11x } \\\Leftrightarrow & 14x \color{blue}{-11x } & = & 3 \color{blue}{+12} \\\Leftrightarrow &3x & = &15\\\Leftrightarrow & \color{red}{3}x & = &15\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{15}{3} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{+10}& = & -6 \color{red}{ +12x } \\\Leftrightarrow & -7x \color{red}{+10}\color{blue}{-10-12x } & = & -6 \color{red}{ +12x }\color{blue}{-10-12x } \\\Leftrightarrow & -7x \color{blue}{-12x } & = & -6 \color{blue}{-10} \\\Leftrightarrow &-19x & = &-16\\\Leftrightarrow & \color{red}{-19}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-16}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{16}{19} } & & \\ & V = \left\{ \frac{16}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{+9}& = & 1 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+9}\color{blue}{-9+13x } & = & 1 \color{red}{ -13x }\color{blue}{-9+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 1 \color{blue}{-9} \\\Leftrightarrow &27x & = &-8\\\Leftrightarrow & \color{red}{27}x & = &-8\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-8}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{27} } & & \\ & V = \left\{ \frac{-8}{27} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-12}& = & -2 \color{red}{ +3x } \\\Leftrightarrow & -14x \color{red}{-12}\color{blue}{+12-3x } & = & -2 \color{red}{ +3x }\color{blue}{+12-3x } \\\Leftrightarrow & -14x \color{blue}{-3x } & = & -2 \color{blue}{+12} \\\Leftrightarrow &-17x & = &10\\\Leftrightarrow & \color{red}{-17}x & = &10\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{10}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{17} } & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{+5}& = & -4 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+5}\color{blue}{-5+4x } & = & -4 \color{red}{ -4x }\color{blue}{-5+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -4 \color{blue}{-5} \\\Leftrightarrow &13x & = &-9\\\Leftrightarrow & \color{red}{13}x & = &-9\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-9}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)