Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{+15}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+15}\color{blue}{-15-x } & = & 2 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 2 \color{blue}{-15} \\\Leftrightarrow &-13x & = &-13\\\Leftrightarrow & \color{red}{-13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-13}{-13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{-5}& = & 12 \color{red}{ +7x } \\\Leftrightarrow & 8x \color{red}{-5}\color{blue}{+5-7x } & = & 12 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & 8x \color{blue}{-7x } & = & 12 \color{blue}{+5} \\\Leftrightarrow &x & = &17\\\Leftrightarrow & \color{red}{}x & = &17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 17 \\\Leftrightarrow & \color{green}{ x = 17 } & & \\ & V = \left\{ 17 \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{+9}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+9}\color{blue}{-9-x } & = & 8 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 8 \color{blue}{-9} \\\Leftrightarrow &-9x & = &-1\\\Leftrightarrow & \color{red}{-9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{+7}& = & -4 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+7}\color{blue}{-7+9x } & = & -4 \color{red}{ -9x }\color{blue}{-7+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & -4 \color{blue}{-7} \\\Leftrightarrow &19x & = &-11\\\Leftrightarrow & \color{red}{19}x & = &-11\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-11}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{19} } & & \\ & V = \left\{ \frac{-11}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{+15}& = & 1 \color{red}{ -8x } \\\Leftrightarrow & -x \color{red}{+15}\color{blue}{-15+8x } & = & 1 \color{red}{ -8x }\color{blue}{-15+8x } \\\Leftrightarrow & -x \color{blue}{+8x } & = & 1 \color{blue}{-15} \\\Leftrightarrow &7x & = &-14\\\Leftrightarrow & \color{red}{7}x & = &-14\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-14}{7} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{+10}& = & -4 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+10}\color{blue}{-10-13x } & = & -4 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -4 \color{blue}{-10} \\\Leftrightarrow &-28x & = &-14\\\Leftrightarrow & \color{red}{-28}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-14}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{+4}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+4}\color{blue}{-4-x } & = & -6 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -6 \color{blue}{-4} \\\Leftrightarrow &x & = &-10\\\Leftrightarrow & \color{red}{}x & = &-10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -10 \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{-2}& = & -6 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-2}\color{blue}{+2+14x } & = & -6 \color{red}{ -14x }\color{blue}{+2+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & -6 \color{blue}{+2} \\\Leftrightarrow &19x & = &-4\\\Leftrightarrow & \color{red}{19}x & = &-4\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-4}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{19} } & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+6}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+6}\color{blue}{-6-x } & = & -12 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -12 \color{blue}{-6} \\\Leftrightarrow &-14x & = &-18\\\Leftrightarrow & \color{red}{-14}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-18}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-10}& = & 8 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{-10}\color{blue}{+10-5x } & = & 8 \color{red}{ +5x }\color{blue}{+10-5x } \\\Leftrightarrow & 14x \color{blue}{-5x } & = & 8 \color{blue}{+10} \\\Leftrightarrow &9x & = &18\\\Leftrightarrow & \color{red}{9}x & = &18\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{18}{9} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{+1}& = & 8 \color{red}{ +6x } \\\Leftrightarrow & 11x \color{red}{+1}\color{blue}{-1-6x } & = & 8 \color{red}{ +6x }\color{blue}{-1-6x } \\\Leftrightarrow & 11x \color{blue}{-6x } & = & 8 \color{blue}{-1} \\\Leftrightarrow &5x & = &7\\\Leftrightarrow & \color{red}{5}x & = &7\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{7}{5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-3}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-3}\color{blue}{+3-x } & = & 3 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 3 \color{blue}{+3} \\\Leftrightarrow &x & = &6\\\Leftrightarrow & \color{red}{}x & = &6\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 6 \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)