Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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