Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-6x-6)& = & 8 \color{red}{-} (-8-5x) \\\Leftrightarrow & -36x-36& = &8+8+5x \\\Leftrightarrow & -36x \color{red}{-36} & = &16 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{-36} \color{blue}{+36} \color{blue}{-5x} & = &16 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+36} \\\Leftrightarrow & -36x-5x& = &16+36 \\\Leftrightarrow & -41x& = &52 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{52}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{-52}{41} & & \\ & V = \left\{ \frac{-52}{41} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (6x-4)& = & -13 \color{red}{-} (12+x) \\\Leftrightarrow & 18x-12& = &-13-12-x \\\Leftrightarrow & 18x \color{red}{-12} & = &-25 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-25 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 18x+x& = &-25+12 \\\Leftrightarrow & 19x& = &-13 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-13}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-13}{19} & & \\ & V = \left\{ \frac{-13}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-5x-2)& = & -6 \color{red}{+} (-2+x) \\\Leftrightarrow & -20x-8& = &-6-2+x \\\Leftrightarrow & -20x \color{red}{-8} & = &-8 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -20x-x& = &-8+8 \\\Leftrightarrow & -21x& = &0 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{0}{ \color{red}{-21} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (4x-1)& = & 6 \color{red}{+} (11+x) \\\Leftrightarrow & 16x-4& = &6+11+x \\\Leftrightarrow & 16x \color{red}{-4} & = &17 \color{red}{+x} \\\Leftrightarrow & 16x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 16x-x& = &17+4 \\\Leftrightarrow & 15x& = &21 \\\Leftrightarrow & \frac{15x}{ \color{red}{15} }& = &\frac{21}{ \color{red}{15} } \\\Leftrightarrow & x = \frac{7}{5} & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-6x+6)& = & 9 \color{red}{+} (1+x) \\\Leftrightarrow & -30x+30& = &9+1+x \\\Leftrightarrow & -30x \color{red}{+30} & = &10 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -30x-x& = &10-30 \\\Leftrightarrow & -31x& = &-20 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-20}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{20}{31} & & \\ & V = \left\{ \frac{20}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (5x-1)& = & -12 \color{red}{+} (-6-3x) \\\Leftrightarrow & 10x-2& = &-12-6-3x \\\Leftrightarrow & 10x \color{red}{-2} & = &-18 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-2} \color{blue}{+2} \color{blue}{+3x} & = &-18 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+2} \\\Leftrightarrow & 10x+3x& = &-18+2 \\\Leftrightarrow & 13x& = &-16 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-16}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-16}{13} & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-4x-6)& = & 15 \color{red}{+} (5-5x) \\\Leftrightarrow & -8x-12& = &15+5-5x \\\Leftrightarrow & -8x \color{red}{-12} & = &20 \color{red}{-5x} \\\Leftrightarrow & -8x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &20 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & -8x+5x& = &20+12 \\\Leftrightarrow & -3x& = &32 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{32}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-32}{3} & & \\ & V = \left\{ \frac{-32}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (5x+6)& = & -11 \color{red}{+} (-4-2x) \\\Leftrightarrow & 15x+18& = &-11-4-2x \\\Leftrightarrow & 15x \color{red}{+18} & = &-15 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+18} \color{blue}{-18} \color{blue}{+2x} & = &-15 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-18} \\\Leftrightarrow & 15x+2x& = &-15-18 \\\Leftrightarrow & 17x& = &-33 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-33}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-33}{17} & & \\ & V = \left\{ \frac{-33}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-3x+5)& = & 13 \color{red}{-} (-1+x) \\\Leftrightarrow & -15x+25& = &13+1-x \\\Leftrightarrow & -15x \color{red}{+25} & = &14 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{+25} \color{blue}{-25} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{-25} \\\Leftrightarrow & -15x+x& = &14-25 \\\Leftrightarrow & -14x& = &-11 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{-11}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{11}{14} & & \\ & V = \left\{ \frac{11}{14} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (6x+2)& = & 6 \color{red}{+} (-7-5x) \\\Leftrightarrow & 36x+12& = &6-7-5x \\\Leftrightarrow & 36x \color{red}{+12} & = &-1 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &-1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & 36x+5x& = &-1-12 \\\Leftrightarrow & 41x& = &-13 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{-13}{ \color{red}{41} } \\\Leftrightarrow & x = \frac{-13}{41} & & \\ & V = \left\{ \frac{-13}{41} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (3x-2)& = & -8 \color{red}{+} (15+x) \\\Leftrightarrow & 12x-8& = &-8+15+x \\\Leftrightarrow & 12x \color{red}{-8} & = &7 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 12x-x& = &7+8 \\\Leftrightarrow & 11x& = &15 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{15}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{15}{11} & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (5x-4)& = & -5 \color{red}{+} (-1-2x) \\\Leftrightarrow & 15x-12& = &-5-1-2x \\\Leftrightarrow & 15x \color{red}{-12} & = &-6 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-12} \color{blue}{+12} \color{blue}{+2x} & = &-6 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+12} \\\Leftrightarrow & 15x+2x& = &-6+12 \\\Leftrightarrow & 17x& = &6 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{6}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{6}{17} & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)