Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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