Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{-14}& = & 2 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-14}\color{blue}{+14+7x } & = & 2 \color{red}{ -7x }\color{blue}{+14+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 2 \color{blue}{+14} \\\Leftrightarrow &22x & = &16\\\Leftrightarrow & \color{red}{22}x & = &16\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{16}{22} \\\Leftrightarrow & \color{green}{ x = \frac{8}{11} } & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{+6}& = & -9 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{+6}\color{blue}{-6+10x } & = & -9 \color{red}{ -10x }\color{blue}{-6+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & -9 \color{blue}{-6} \\\Leftrightarrow &21x & = &-15\\\Leftrightarrow & \color{red}{21}x & = &-15\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-15}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{-12}& = & -6 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-12}\color{blue}{+12+7x } & = & -6 \color{red}{ -7x }\color{blue}{+12+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -6 \color{blue}{+12} \\\Leftrightarrow &15x & = &6\\\Leftrightarrow & \color{red}{15}x & = &6\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{6}{15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{-5}& = & -3 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{-5}\color{blue}{+5+14x } & = & -3 \color{red}{ -14x }\color{blue}{+5+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & -3 \color{blue}{+5} \\\Leftrightarrow &17x & = &2\\\Leftrightarrow & \color{red}{17}x & = &2\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{2}{17} \\\Leftrightarrow & \color{green}{ x = \frac{2}{17} } & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{-15}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-15}\color{blue}{+15-x } & = & -6 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -6 \color{blue}{+15} \\\Leftrightarrow &7x & = &9\\\Leftrightarrow & \color{red}{7}x & = &9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{+10}& = & 10 \color{red}{ +8x } \\\Leftrightarrow & 15x \color{red}{+10}\color{blue}{-10-8x } & = & 10 \color{red}{ +8x }\color{blue}{-10-8x } \\\Leftrightarrow & 15x \color{blue}{-8x } & = & 10 \color{blue}{-10} \\\Leftrightarrow &7x & = &0\\\Leftrightarrow & \color{red}{7}x & = &0\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{0}{7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{-11}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & -2x \color{red}{-11}\color{blue}{+11-7x } & = & 13 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & -2x \color{blue}{-7x } & = & 13 \color{blue}{+11} \\\Leftrightarrow &-9x & = &24\\\Leftrightarrow & \color{red}{-9}x & = &24\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{24}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{-7}& = & 12 \color{red}{ +7x } \\\Leftrightarrow & 5x \color{red}{-7}\color{blue}{+7-7x } & = & 12 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & 5x \color{blue}{-7x } & = & 12 \color{blue}{+7} \\\Leftrightarrow &-2x & = &19\\\Leftrightarrow & \color{red}{-2}x & = &19\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{19}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{2} } & & \\ & V = \left\{ \frac{-19}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{-6}& = & -6 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{-6}\color{blue}{+6+15x } & = & -6 \color{red}{ -15x }\color{blue}{+6+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & -6 \color{blue}{+6} \\\Leftrightarrow &19x & = &0\\\Leftrightarrow & \color{red}{19}x & = &0\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{0}{19} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{-9}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{-9}\color{blue}{+9-7x } & = & 4 \color{red}{ +7x }\color{blue}{+9-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & 4 \color{blue}{+9} \\\Leftrightarrow &-10x & = &13\\\Leftrightarrow & \color{red}{-10}x & = &13\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{13}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{10} } & & \\ & V = \left\{ \frac{-13}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{-9}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-9}\color{blue}{+9-x } & = & -10 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -10 \color{blue}{+9} \\\Leftrightarrow &-12x & = &-1\\\Leftrightarrow & \color{red}{-12}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-1}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{12} } & & \\ & V = \left\{ \frac{1}{12} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{+12}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+12}\color{blue}{-12-x } & = & 14 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 14 \color{blue}{-12} \\\Leftrightarrow &-3x & = &2\\\Leftrightarrow & \color{red}{-3}x & = &2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)