Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{-10}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-10}\color{blue}{+10-x } & = & 5 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 5 \color{blue}{+10} \\\Leftrightarrow &-6x & = &15\\\Leftrightarrow & \color{red}{-6}x & = &15\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{15}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{-11}& = & 9 \color{red}{ +9x } \\\Leftrightarrow & -13x \color{red}{-11}\color{blue}{+11-9x } & = & 9 \color{red}{ +9x }\color{blue}{+11-9x } \\\Leftrightarrow & -13x \color{blue}{-9x } & = & 9 \color{blue}{+11} \\\Leftrightarrow &-22x & = &20\\\Leftrightarrow & \color{red}{-22}x & = &20\\\Leftrightarrow & \frac{\color{red}{-22}x}{ \color{blue}{ -22}} & = & \frac{20}{-22} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{11} } & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{-3}& = & 2 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{-3}\color{blue}{+3+6x } & = & 2 \color{red}{ -6x }\color{blue}{+3+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & 2 \color{blue}{+3} \\\Leftrightarrow &13x & = &5\\\Leftrightarrow & \color{red}{13}x & = &5\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{5}{13} \\\Leftrightarrow & \color{green}{ x = \frac{5}{13} } & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{-11}& = & -14 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{-11}\color{blue}{+11-3x } & = & -14 \color{red}{ +3x }\color{blue}{+11-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & -14 \color{blue}{+11} \\\Leftrightarrow &-14x & = &-3\\\Leftrightarrow & \color{red}{-14}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{14} } & & \\ & V = \left\{ \frac{3}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{+2}& = & 15 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{+2}\color{blue}{-2+10x } & = & 15 \color{red}{ -10x }\color{blue}{-2+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & 15 \color{blue}{-2} \\\Leftrightarrow &17x & = &13\\\Leftrightarrow & \color{red}{17}x & = &13\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{13}{17} \\\Leftrightarrow & \color{green}{ x = \frac{13}{17} } & & \\ & V = \left\{ \frac{13}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{-5}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-5}\color{blue}{+5-x } & = & 12 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 12 \color{blue}{+5} \\\Leftrightarrow &7x & = &17\\\Leftrightarrow & \color{red}{7}x & = &17\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{17}{7} \\\Leftrightarrow & \color{green}{ x = \frac{17}{7} } & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{-2}& = & -8 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{-2}\color{blue}{+2-4x } & = & -8 \color{red}{ +4x }\color{blue}{+2-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & -8 \color{blue}{+2} \\\Leftrightarrow &-7x & = &-6\\\Leftrightarrow & \color{red}{-7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{-4}& = & 9 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{-4}\color{blue}{+4-11x } & = & 9 \color{red}{ +11x }\color{blue}{+4-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & 9 \color{blue}{+4} \\\Leftrightarrow &-6x & = &13\\\Leftrightarrow & \color{red}{-6}x & = &13\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{13}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{-12}& = & 11 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12-4x } & = & 11 \color{red}{ +4x }\color{blue}{+12-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & 11 \color{blue}{+12} \\\Leftrightarrow &-x & = &23\\\Leftrightarrow & \color{red}{-}x & = &23\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{23}{-1} \\\Leftrightarrow & \color{green}{ x = -23 } & & \\ & V = \left\{ -23 \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{+1}& = & 12 \color{red}{ +8x } \\\Leftrightarrow & x \color{red}{+1}\color{blue}{-1-8x } & = & 12 \color{red}{ +8x }\color{blue}{-1-8x } \\\Leftrightarrow & x \color{blue}{-8x } & = & 12 \color{blue}{-1} \\\Leftrightarrow &-7x & = &11\\\Leftrightarrow & \color{red}{-7}x & = &11\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{11}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{7} } & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-1}& = & 6 \color{red}{ -3x } \\\Leftrightarrow & 13x \color{red}{-1}\color{blue}{+1+3x } & = & 6 \color{red}{ -3x }\color{blue}{+1+3x } \\\Leftrightarrow & 13x \color{blue}{+3x } & = & 6 \color{blue}{+1} \\\Leftrightarrow &16x & = &7\\\Leftrightarrow & \color{red}{16}x & = &7\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{7}{16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{16} } & & \\ & V = \left\{ \frac{7}{16} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{-3}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-3}\color{blue}{+3-x } & = & -6 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -6 \color{blue}{+3} \\\Leftrightarrow &-14x & = &-3\\\Leftrightarrow & \color{red}{-14}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{14} } & & \\ & V = \left\{ \frac{3}{14} \right\} & \\\end{align}\)