Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{-4}& = & -14 \color{red}{ +3x } \\\Leftrightarrow & x \color{red}{-4}\color{blue}{+4-3x } & = & -14 \color{red}{ +3x }\color{blue}{+4-3x } \\\Leftrightarrow & x \color{blue}{-3x } & = & -14 \color{blue}{+4} \\\Leftrightarrow &-2x & = &-10\\\Leftrightarrow & \color{red}{-2}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-10}{-2} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{+8}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+8}\color{blue}{-8-x } & = & 7 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 7 \color{blue}{-8} \\\Leftrightarrow &-11x & = &-1\\\Leftrightarrow & \color{red}{-11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{+12}& = & 12 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+12}\color{blue}{-12+7x } & = & 12 \color{red}{ -7x }\color{blue}{-12+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 12 \color{blue}{-12} \\\Leftrightarrow &15x & = &0\\\Leftrightarrow & \color{red}{15}x & = &0\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{0}{15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{+11}& = & 2 \color{red}{ -14x } \\\Leftrightarrow & -x \color{red}{+11}\color{blue}{-11+14x } & = & 2 \color{red}{ -14x }\color{blue}{-11+14x } \\\Leftrightarrow & -x \color{blue}{+14x } & = & 2 \color{blue}{-11} \\\Leftrightarrow &13x & = &-9\\\Leftrightarrow & \color{red}{13}x & = &-9\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-9}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{-3}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{-3}\color{blue}{+3-13x } & = & -10 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & -10 \color{blue}{+3} \\\Leftrightarrow &-3x & = &-7\\\Leftrightarrow & \color{red}{-3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{+7}& = & -5 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+7}\color{blue}{-7-9x } & = & -5 \color{red}{ +9x }\color{blue}{-7-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -5 \color{blue}{-7} \\\Leftrightarrow &-17x & = &-12\\\Leftrightarrow & \color{red}{-17}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-12}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{12}{17} } & & \\ & V = \left\{ \frac{12}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{-1}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{-1}\color{blue}{+1-x } & = & -7 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & -7 \color{blue}{+1} \\\Leftrightarrow &4x & = &-6\\\Leftrightarrow & \color{red}{4}x & = &-6\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-6}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{+2}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+2}\color{blue}{-2-x } & = & 6 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 6 \color{blue}{-2} \\\Leftrightarrow &-9x & = &4\\\Leftrightarrow & \color{red}{-9}x & = &4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{-4}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-4}\color{blue}{+4-x } & = & -12 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -12 \color{blue}{+4} \\\Leftrightarrow &-3x & = &-8\\\Leftrightarrow & \color{red}{-3}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+9}& = & 14 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+9}\color{blue}{-9-x } & = & 14 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & 14 \color{blue}{-9} \\\Leftrightarrow &12x & = &5\\\Leftrightarrow & \color{red}{12}x & = &5\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{5}{12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{12} } & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{-1}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-1}\color{blue}{+1-x } & = & 3 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 3 \color{blue}{+1} \\\Leftrightarrow &-6x & = &4\\\Leftrightarrow & \color{red}{-6}x & = &4\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{4}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{-12}& = & -8 \color{red}{ +9x } \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12-9x } & = & -8 \color{red}{ +9x }\color{blue}{+12-9x } \\\Leftrightarrow & 11x \color{blue}{-9x } & = & -8 \color{blue}{+12} \\\Leftrightarrow &2x & = &4\\\Leftrightarrow & \color{red}{2}x & = &4\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{4}{2} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)