Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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