Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{+3}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+3}\color{blue}{-3-x } & = & -4 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -4 \color{blue}{-3} \\\Leftrightarrow &-6x & = &-7\\\Leftrightarrow & \color{red}{-6}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-7}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{-13}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-13}\color{blue}{+13-x } & = & 13 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 13 \color{blue}{+13} \\\Leftrightarrow &x & = &26\\\Leftrightarrow & \color{red}{}x & = &26\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 26 \\\Leftrightarrow & \color{green}{ x = 26 } & & \\ & V = \left\{ 26 \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{-6}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6-x } & = & -1 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -1 \color{blue}{+6} \\\Leftrightarrow &-13x & = &5\\\Leftrightarrow & \color{red}{-13}x & = &5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{-9}& = & -6 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{-9}\color{blue}{+9-13x } & = & -6 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & -6 \color{blue}{+9} \\\Leftrightarrow &-x & = &3\\\Leftrightarrow & \color{red}{-}x & = &3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{3}{-1} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{+14}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14-7x } & = & -1 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -1 \color{blue}{-14} \\\Leftrightarrow &-20x & = &-15\\\Leftrightarrow & \color{red}{-20}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-15}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{+12}& = & 11 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+12}\color{blue}{-12+7x } & = & 11 \color{red}{ -7x }\color{blue}{-12+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &19x & = &-1\\\Leftrightarrow & \color{red}{19}x & = &-1\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-1}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{19} } & & \\ & V = \left\{ \frac{-1}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+1}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+1}\color{blue}{-1-x } & = & 7 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 7 \color{blue}{-1} \\\Leftrightarrow &-16x & = &6\\\Leftrightarrow & \color{red}{-16}x & = &6\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{6}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{-1}& = & -11 \color{red}{ -10x } \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1+10x } & = & -11 \color{red}{ -10x }\color{blue}{+1+10x } \\\Leftrightarrow & -x \color{blue}{+10x } & = & -11 \color{blue}{+1} \\\Leftrightarrow &9x & = &-10\\\Leftrightarrow & \color{red}{9}x & = &-10\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-10}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{9} } & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{-9}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-9}\color{blue}{+9-x } & = & 1 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 1 \color{blue}{+9} \\\Leftrightarrow &-5x & = &10\\\Leftrightarrow & \color{red}{-5}x & = &10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{10}{-5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{+11}& = & 5 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+11}\color{blue}{-11+7x } & = & 5 \color{red}{ -7x }\color{blue}{-11+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 5 \color{blue}{-11} \\\Leftrightarrow &22x & = &-6\\\Leftrightarrow & \color{red}{22}x & = &-6\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-6}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+11}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+11}\color{blue}{-11-x } & = & -7 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -7 \color{blue}{-11} \\\Leftrightarrow &-11x & = &-18\\\Leftrightarrow & \color{red}{-11}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-18}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{18}{11} } & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{+11}& = & 8 \color{red}{ +2x } \\\Leftrightarrow & 9x \color{red}{+11}\color{blue}{-11-2x } & = & 8 \color{red}{ +2x }\color{blue}{-11-2x } \\\Leftrightarrow & 9x \color{blue}{-2x } & = & 8 \color{blue}{-11} \\\Leftrightarrow &7x & = &-3\\\Leftrightarrow & \color{red}{7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-3}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)