Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{-6}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & 13x \color{red}{-6}\color{blue}{+6-11x } & = & -3 \color{red}{ +11x }\color{blue}{+6-11x } \\\Leftrightarrow & 13x \color{blue}{-11x } & = & -3 \color{blue}{+6} \\\Leftrightarrow &2x & = &3\\\Leftrightarrow & \color{red}{2}x & = &3\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{3}{2} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{-10}& = & -15 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-10}\color{blue}{+10-13x } & = & -15 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & -15 \color{blue}{+10} \\\Leftrightarrow &-17x & = &-5\\\Leftrightarrow & \color{red}{-17}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-5}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{5}{17} } & & \\ & V = \left\{ \frac{5}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{+14}& = & 8 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+14}\color{blue}{-14-5x } & = & 8 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & 8 \color{blue}{-14} \\\Leftrightarrow &7x & = &-6\\\Leftrightarrow & \color{red}{7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-6}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{-6}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-6}\color{blue}{+6-x } & = & -10 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -10 \color{blue}{+6} \\\Leftrightarrow &x & = &-4\\\Leftrightarrow & \color{red}{}x & = &-4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -4 \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+4}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{+4}\color{blue}{-4-x } & = & 10 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & 10 \color{blue}{-4} \\\Leftrightarrow &3x & = &6\\\Leftrightarrow & \color{red}{3}x & = &6\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{6}{3} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-1}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-1}\color{blue}{+1-7x } & = & 13 \color{red}{ +7x }\color{blue}{+1-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 13 \color{blue}{+1} \\\Leftrightarrow &-20x & = &14\\\Leftrightarrow & \color{red}{-20}x & = &14\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{14}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{10} } & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{-10}& = & -6 \color{red}{ +10x } \\\Leftrightarrow & x \color{red}{-10}\color{blue}{+10-10x } & = & -6 \color{red}{ +10x }\color{blue}{+10-10x } \\\Leftrightarrow & x \color{blue}{-10x } & = & -6 \color{blue}{+10} \\\Leftrightarrow &-9x & = &4\\\Leftrightarrow & \color{red}{-9}x & = &4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{-4}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-4}\color{blue}{+4-x } & = & 3 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 3 \color{blue}{+4} \\\Leftrightarrow &-10x & = &7\\\Leftrightarrow & \color{red}{-10}x & = &7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{10} } & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+3}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+3}\color{blue}{-3-x } & = & -13 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -13 \color{blue}{-3} \\\Leftrightarrow &-14x & = &-16\\\Leftrightarrow & \color{red}{-14}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-16}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{+6}& = & 2 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{+6}\color{blue}{-6-6x } & = & 2 \color{red}{ +6x }\color{blue}{-6-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & 2 \color{blue}{-6} \\\Leftrightarrow &-x & = &-4\\\Leftrightarrow & \color{red}{-}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-4}{-1} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{+9}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+9}\color{blue}{-9-x } & = & -4 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -4 \color{blue}{-9} \\\Leftrightarrow &-4x & = &-13\\\Leftrightarrow & \color{red}{-4}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-13}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{13}{4} } & & \\ & V = \left\{ \frac{13}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{-11}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-11}\color{blue}{+11-x } & = & 10 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 10 \color{blue}{+11} \\\Leftrightarrow &-9x & = &21\\\Leftrightarrow & \color{red}{-9}x & = &21\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{21}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)