Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{-1}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{-1}\color{blue}{+1-x } & = & 13 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & 13 \color{blue}{+1} \\\Leftrightarrow &6x & = &14\\\Leftrightarrow & \color{red}{6}x & = &14\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{14}{6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{-3}& = & -10 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{-3}\color{blue}{+3-3x } & = & -10 \color{red}{ +3x }\color{blue}{+3-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & -10 \color{blue}{+3} \\\Leftrightarrow &-x & = &-7\\\Leftrightarrow & \color{red}{-}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-7}{-1} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-10}& = & -7 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{-10}\color{blue}{+10+2x } & = & -7 \color{red}{ -2x }\color{blue}{+10+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & -7 \color{blue}{+10} \\\Leftrightarrow &13x & = &3\\\Leftrightarrow & \color{red}{13}x & = &3\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{3}{13} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{-2}& = & 6 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-2}\color{blue}{+2+12x } & = & 6 \color{red}{ -12x }\color{blue}{+2+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & 6 \color{blue}{+2} \\\Leftrightarrow &25x & = &8\\\Leftrightarrow & \color{red}{25}x & = &8\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{8}{25} \\\Leftrightarrow & \color{green}{ x = \frac{8}{25} } & & \\ & V = \left\{ \frac{8}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{-9}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-9}\color{blue}{+9-x } & = & -15 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -15 \color{blue}{+9} \\\Leftrightarrow &-15x & = &-6\\\Leftrightarrow & \color{red}{-15}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{-9}& = & 2 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-9}\color{blue}{+9-9x } & = & 2 \color{red}{ +9x }\color{blue}{+9-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 2 \color{blue}{+9} \\\Leftrightarrow &-17x & = &11\\\Leftrightarrow & \color{red}{-17}x & = &11\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{11}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{17} } & & \\ & V = \left\{ \frac{-11}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{+12}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+12}\color{blue}{-12-x } & = & 5 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 5 \color{blue}{-12} \\\Leftrightarrow &-15x & = &-7\\\Leftrightarrow & \color{red}{-15}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{15} } & & \\ & V = \left\{ \frac{7}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-1}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-1}\color{blue}{+1-x } & = & 9 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 9 \color{blue}{+1} \\\Leftrightarrow &-11x & = &10\\\Leftrightarrow & \color{red}{-11}x & = &10\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{10}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{11} } & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{+4}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+4}\color{blue}{-4-x } & = & -5 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -5 \color{blue}{-4} \\\Leftrightarrow &-13x & = &-9\\\Leftrightarrow & \color{red}{-13}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{9}{13} } & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{-11}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{-11}\color{blue}{+11-7x } & = & 4 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & 4 \color{blue}{+11} \\\Leftrightarrow &5x & = &15\\\Leftrightarrow & \color{red}{5}x & = &15\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{15}{5} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+10}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+10}\color{blue}{-10-7x } & = & 11 \color{red}{ +7x }\color{blue}{-10-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 11 \color{blue}{-10} \\\Leftrightarrow &3x & = &1\\\Leftrightarrow & \color{red}{3}x & = &1\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{1}{3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{-3}& = & 2 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-3}\color{blue}{+3+11x } & = & 2 \color{red}{ -11x }\color{blue}{+3+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & 2 \color{blue}{+3} \\\Leftrightarrow &26x & = &5\\\Leftrightarrow & \color{red}{26}x & = &5\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{5}{26} \\\Leftrightarrow & \color{green}{ x = \frac{5}{26} } & & \\ & V = \left\{ \frac{5}{26} \right\} & \\\end{align}\)