Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{-1}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-1}\color{blue}{+1-x } & = & -7 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -7 \color{blue}{+1} \\\Leftrightarrow &-13x & = &-6\\\Leftrightarrow & \color{red}{-13}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+8}& = & 11 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+8}\color{blue}{-8+7x } & = & 11 \color{red}{ -7x }\color{blue}{-8+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 11 \color{blue}{-8} \\\Leftrightarrow &22x & = &3\\\Leftrightarrow & \color{red}{22}x & = &3\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{3}{22} \\\Leftrightarrow & \color{green}{ x = \frac{3}{22} } & & \\ & V = \left\{ \frac{3}{22} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{-1}& = & 11 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{-1}\color{blue}{+1+12x } & = & 11 \color{red}{ -12x }\color{blue}{+1+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & 11 \color{blue}{+1} \\\Leftrightarrow &17x & = &12\\\Leftrightarrow & \color{red}{17}x & = &12\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{12}{17} \\\Leftrightarrow & \color{green}{ x = \frac{12}{17} } & & \\ & V = \left\{ \frac{12}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{+10}& = & -1 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+10}\color{blue}{-10-5x } & = & -1 \color{red}{ +5x }\color{blue}{-10-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -1 \color{blue}{-10} \\\Leftrightarrow &-14x & = &-11\\\Leftrightarrow & \color{red}{-14}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-11}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{11}{14} } & & \\ & V = \left\{ \frac{11}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{+11}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+11}\color{blue}{-11-x } & = & 1 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 1 \color{blue}{-11} \\\Leftrightarrow &-11x & = &-10\\\Leftrightarrow & \color{red}{-11}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-10}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{+4}& = & -2 \color{red}{ +6x } \\\Leftrightarrow & 13x \color{red}{+4}\color{blue}{-4-6x } & = & -2 \color{red}{ +6x }\color{blue}{-4-6x } \\\Leftrightarrow & 13x \color{blue}{-6x } & = & -2 \color{blue}{-4} \\\Leftrightarrow &7x & = &-6\\\Leftrightarrow & \color{red}{7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-6}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{+4}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+4}\color{blue}{-4-x } & = & 2 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 2 \color{blue}{-4} \\\Leftrightarrow &-8x & = &-2\\\Leftrightarrow & \color{red}{-8}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{+1}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{+1}\color{blue}{-1-13x } & = & -9 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & -9 \color{blue}{-1} \\\Leftrightarrow &-x & = &-10\\\Leftrightarrow & \color{red}{-}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-10}{-1} \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{+13}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+13}\color{blue}{-13-13x } & = & 13 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 13 \color{blue}{-13} \\\Leftrightarrow &-25x & = &0\\\Leftrightarrow & \color{red}{-25}x & = &0\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{0}{-25} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{+15}& = & -13 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{+15}\color{blue}{-15+8x } & = & -13 \color{red}{ -8x }\color{blue}{-15+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -13 \color{blue}{-15} \\\Leftrightarrow &11x & = &-28\\\Leftrightarrow & \color{red}{11}x & = &-28\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-28}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{11} } & & \\ & V = \left\{ \frac{-28}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{+2}& = & 14 \color{red}{ +7x } \\\Leftrightarrow & x \color{red}{+2}\color{blue}{-2-7x } & = & 14 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & x \color{blue}{-7x } & = & 14 \color{blue}{-2} \\\Leftrightarrow &-6x & = &12\\\Leftrightarrow & \color{red}{-6}x & = &12\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{12}{-6} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{+2}& = & -7 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{+2}\color{blue}{-2-4x } & = & -7 \color{red}{ +4x }\color{blue}{-2-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & -7 \color{blue}{-2} \\\Leftrightarrow &5x & = &-9\\\Leftrightarrow & \color{red}{5}x & = &-9\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-9}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)