Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{-8}& = & -5 \color{red}{ -2x } \\\Leftrightarrow & x \color{red}{-8}\color{blue}{+8+2x } & = & -5 \color{red}{ -2x }\color{blue}{+8+2x } \\\Leftrightarrow & x \color{blue}{+2x } & = & -5 \color{blue}{+8} \\\Leftrightarrow &3x & = &3\\\Leftrightarrow & \color{red}{3}x & = &3\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{3}{3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{-2}& = & 1 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-2}\color{blue}{+2+13x } & = & 1 \color{red}{ -13x }\color{blue}{+2+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & 1 \color{blue}{+2} \\\Leftrightarrow &24x & = &3\\\Leftrightarrow & \color{red}{24}x & = &3\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{3}{24} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{-7}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-7}\color{blue}{+7-x } & = & -8 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -8 \color{blue}{+7} \\\Leftrightarrow &-8x & = &-1\\\Leftrightarrow & \color{red}{-8}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{-5}& = & -10 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{-5}\color{blue}{+5-11x } & = & -10 \color{red}{ +11x }\color{blue}{+5-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & -10 \color{blue}{+5} \\\Leftrightarrow &-18x & = &-5\\\Leftrightarrow & \color{red}{-18}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-5}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{5}{18} } & & \\ & V = \left\{ \frac{5}{18} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{+10}& = & 11 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{+10}\color{blue}{-10+2x } & = & 11 \color{red}{ -2x }\color{blue}{-10+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & 11 \color{blue}{-10} \\\Leftrightarrow &13x & = &1\\\Leftrightarrow & \color{red}{13}x & = &1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+3}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+3}\color{blue}{-3-x } & = & 8 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 8 \color{blue}{-3} \\\Leftrightarrow &-11x & = &5\\\Leftrightarrow & \color{red}{-11}x & = &5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+1}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+1}\color{blue}{-1-x } & = & -12 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -12 \color{blue}{-1} \\\Leftrightarrow &-4x & = &-13\\\Leftrightarrow & \color{red}{-4}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-13}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{13}{4} } & & \\ & V = \left\{ \frac{13}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{-12}& = & 3 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{-12}\color{blue}{+12-4x } & = & 3 \color{red}{ +4x }\color{blue}{+12-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & 3 \color{blue}{+12} \\\Leftrightarrow &-7x & = &15\\\Leftrightarrow & \color{red}{-7}x & = &15\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{15}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{7} } & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+13}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+13}\color{blue}{-13-13x } & = & 3 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 3 \color{blue}{-13} \\\Leftrightarrow &-19x & = &-10\\\Leftrightarrow & \color{red}{-19}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-10}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{10}{19} } & & \\ & V = \left\{ \frac{10}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-1}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-1}\color{blue}{+1-x } & = & -2 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -2 \color{blue}{+1} \\\Leftrightarrow &-13x & = &-1\\\Leftrightarrow & \color{red}{-13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{-12}& = & 1 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{-12}\color{blue}{+12-9x } & = & 1 \color{red}{ +9x }\color{blue}{+12-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & 1 \color{blue}{+12} \\\Leftrightarrow &-x & = &13\\\Leftrightarrow & \color{red}{-}x & = &13\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{13}{-1} \\\Leftrightarrow & \color{green}{ x = -13 } & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{-12}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-12}\color{blue}{+12-x } & = & -8 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -8 \color{blue}{+12} \\\Leftrightarrow &9x & = &4\\\Leftrightarrow & \color{red}{9}x & = &4\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{4}{9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)