Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{-11}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-11}\color{blue}{+11-x } & = & 5 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 5 \color{blue}{+11} \\\Leftrightarrow &13x & = &16\\\Leftrightarrow & \color{red}{13}x & = &16\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{16}{13} \\\Leftrightarrow & \color{green}{ x = \frac{16}{13} } & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{+1}& = & -1 \color{red}{ -2x } \\\Leftrightarrow & x \color{red}{+1}\color{blue}{-1+2x } & = & -1 \color{red}{ -2x }\color{blue}{-1+2x } \\\Leftrightarrow & x \color{blue}{+2x } & = & -1 \color{blue}{-1} \\\Leftrightarrow &3x & = &-2\\\Leftrightarrow & \color{red}{3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-2}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{+11}& = & -4 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+11}\color{blue}{-11+13x } & = & -4 \color{red}{ -13x }\color{blue}{-11+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -4 \color{blue}{-11} \\\Leftrightarrow &27x & = &-15\\\Leftrightarrow & \color{red}{27}x & = &-15\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-15}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{-10}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-10}\color{blue}{+10-x } & = & -12 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -12 \color{blue}{+10} \\\Leftrightarrow &-6x & = &-2\\\Leftrightarrow & \color{red}{-6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{+15}& = & 11 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{+15}\color{blue}{-15-4x } & = & 11 \color{red}{ +4x }\color{blue}{-15-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & 11 \color{blue}{-15} \\\Leftrightarrow &11x & = &-4\\\Leftrightarrow & \color{red}{11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{+8}& = & 11 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{+8}\color{blue}{-8+11x } & = & 11 \color{red}{ -11x }\color{blue}{-8+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & 11 \color{blue}{-8} \\\Leftrightarrow &14x & = &3\\\Leftrightarrow & \color{red}{14}x & = &3\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{3}{14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{14} } & & \\ & V = \left\{ \frac{3}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{-9}& = & -4 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-9}\color{blue}{+9+6x } & = & -4 \color{red}{ -6x }\color{blue}{+9+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -4 \color{blue}{+9} \\\Leftrightarrow &19x & = &5\\\Leftrightarrow & \color{red}{19}x & = &5\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{5}{19} \\\Leftrightarrow & \color{green}{ x = \frac{5}{19} } & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{+4}& = & 12 \color{red}{ +3x } \\\Leftrightarrow & -8x \color{red}{+4}\color{blue}{-4-3x } & = & 12 \color{red}{ +3x }\color{blue}{-4-3x } \\\Leftrightarrow & -8x \color{blue}{-3x } & = & 12 \color{blue}{-4} \\\Leftrightarrow &-11x & = &8\\\Leftrightarrow & \color{red}{-11}x & = &8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{11} } & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{+4}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+4}\color{blue}{-4-x } & = & -9 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -9 \color{blue}{-4} \\\Leftrightarrow &5x & = &-13\\\Leftrightarrow & \color{red}{5}x & = &-13\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-13}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-3}& = & 6 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-3}\color{blue}{+3-13x } & = & 6 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 6 \color{blue}{+3} \\\Leftrightarrow &-25x & = &9\\\Leftrightarrow & \color{red}{-25}x & = &9\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{9}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{25} } & & \\ & V = \left\{ \frac{-9}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+1}& = & 13 \color{red}{ +9x } \\\Leftrightarrow & 10x \color{red}{+1}\color{blue}{-1-9x } & = & 13 \color{red}{ +9x }\color{blue}{-1-9x } \\\Leftrightarrow & 10x \color{blue}{-9x } & = & 13 \color{blue}{-1} \\\Leftrightarrow &x & = &12\\\Leftrightarrow & \color{red}{}x & = &12\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 12 \\\Leftrightarrow & \color{green}{ x = 12 } & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{-7}& = & 9 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-7}\color{blue}{+7-7x } & = & 9 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 9 \color{blue}{+7} \\\Leftrightarrow &-17x & = &16\\\Leftrightarrow & \color{red}{-17}x & = &16\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{16}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{17} } & & \\ & V = \left\{ \frac{-16}{17} \right\} & \\\end{align}\)