Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(11x-2=4+x\)
2. \(-12x-14=-6+5x\)
3. \(-x-8=10+0x\)
4. \(-14x-9=-5+x\)
5. \(-11x-1=5+x\)
6. \(-7x+1=-5+11x\)
7. \(-3x+15=2+x\)
8. \(11x-15=7+4x\)
9. \(x-15=10-6x\)
10. \(-x-7=5+4x\)
11. \(13x+2=-3-12x\)
12. \(-5x-1=2+11x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{-2}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{-2}\color{blue}{+2-x } & = & 4 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & 4 \color{blue}{+2} \\\Leftrightarrow &10x & = &6\\\Leftrightarrow & \color{red}{10}x & = &6\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{6}{10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{-14}& = & -6 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{-14}\color{blue}{+14-5x } & = & -6 \color{red}{ +5x }\color{blue}{+14-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & -6 \color{blue}{+14} \\\Leftrightarrow &-17x & = &8\\\Leftrightarrow & \color{red}{-17}x & = &8\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{8}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{17} } & & \\ & V = \left\{ \frac{-8}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{-8}& = & 10 \color{red}{ +0x } \\\Leftrightarrow & -x \color{red}{-8}\color{blue}{+8+0x } & = & 10 \color{red}{ +0x }\color{blue}{+8+0x } \\\Leftrightarrow & -x \color{blue}{+0x } & = & 10 \color{blue}{+8} \\\Leftrightarrow &-x & = &18\\\Leftrightarrow & \color{red}{-}x & = &18\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{18}{-1} \\\Leftrightarrow & \color{green}{ x = -18 } & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{-9}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-9}\color{blue}{+9-x } & = & -5 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -5 \color{blue}{+9} \\\Leftrightarrow &-15x & = &4\\\Leftrightarrow & \color{red}{-15}x & = &4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{-1}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-1}\color{blue}{+1-x } & = & 5 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 5 \color{blue}{+1} \\\Leftrightarrow &-12x & = &6\\\Leftrightarrow & \color{red}{-12}x & = &6\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{6}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{+1}& = & -5 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1-11x } & = & -5 \color{red}{ +11x }\color{blue}{-1-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & -5 \color{blue}{-1} \\\Leftrightarrow &-18x & = &-6\\\Leftrightarrow & \color{red}{-18}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-6}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+15}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+15}\color{blue}{-15-x } & = & 2 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 2 \color{blue}{-15} \\\Leftrightarrow &-4x & = &-13\\\Leftrightarrow & \color{red}{-4}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-13}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{13}{4} } & & \\ & V = \left\{ \frac{13}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{-15}& = & 7 \color{red}{ +4x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15-4x } & = & 7 \color{red}{ +4x }\color{blue}{+15-4x } \\\Leftrightarrow & 11x \color{blue}{-4x } & = & 7 \color{blue}{+15} \\\Leftrightarrow &7x & = &22\\\Leftrightarrow & \color{red}{7}x & = &22\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{22}{7} \\\Leftrightarrow & \color{green}{ x = \frac{22}{7} } & & \\ & V = \left\{ \frac{22}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{-15}& = & 10 \color{red}{ -6x } \\\Leftrightarrow & x \color{red}{-15}\color{blue}{+15+6x } & = & 10 \color{red}{ -6x }\color{blue}{+15+6x } \\\Leftrightarrow & x \color{blue}{+6x } & = & 10 \color{blue}{+15} \\\Leftrightarrow &7x & = &25\\\Leftrightarrow & \color{red}{7}x & = &25\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{25}{7} \\\Leftrightarrow & \color{green}{ x = \frac{25}{7} } & & \\ & V = \left\{ \frac{25}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{-7}& = & 5 \color{red}{ +4x } \\\Leftrightarrow & -x \color{red}{-7}\color{blue}{+7-4x } & = & 5 \color{red}{ +4x }\color{blue}{+7-4x } \\\Leftrightarrow & -x \color{blue}{-4x } & = & 5 \color{blue}{+7} \\\Leftrightarrow &-5x & = &12\\\Leftrightarrow & \color{red}{-5}x & = &12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{+2}& = & -3 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{+2}\color{blue}{-2+12x } & = & -3 \color{red}{ -12x }\color{blue}{-2+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & -3 \color{blue}{-2} \\\Leftrightarrow &25x & = &-5\\\Leftrightarrow & \color{red}{25}x & = &-5\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-5}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{-1}& = & 2 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{-1}\color{blue}{+1-11x } & = & 2 \color{red}{ +11x }\color{blue}{+1-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & 2 \color{blue}{+1} \\\Leftrightarrow &-16x & = &3\\\Leftrightarrow & \color{red}{-16}x & = &3\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{3}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{16} } & & \\ & V = \left\{ \frac{-3}{16} \right\} & \\\end{align}\)