Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (3x-5)& = & 12 \color{red}{-} (10-5x) \\\Leftrightarrow & 6x-10& = &12-10+5x \\\Leftrightarrow & 6x \color{red}{-10} & = &2 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-10} \color{blue}{+10} \color{blue}{-5x} & = &2 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+10} \\\Leftrightarrow & 6x-5x& = &2+10 \\\Leftrightarrow & x& = &12 \\ & V = \left\{ 12 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (3x-4)& = & -13 \color{red}{+} (10+x) \\\Leftrightarrow & 12x-16& = &-13+10+x \\\Leftrightarrow & 12x \color{red}{-16} & = &-3 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & 12x-x& = &-3+16 \\\Leftrightarrow & 11x& = &13 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{13}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{13}{11} & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-3x-1)& = & -9 \color{red}{-} (9+x) \\\Leftrightarrow & -15x-5& = &-9-9-x \\\Leftrightarrow & -15x \color{red}{-5} & = &-18 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & -15x+x& = &-18+5 \\\Leftrightarrow & -14x& = &-13 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{-13}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{13}{14} & & \\ & V = \left\{ \frac{13}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-2x+2)& = & -5 \color{red}{+} (-10+x) \\\Leftrightarrow & -8x+8& = &-5-10+x \\\Leftrightarrow & -8x \color{red}{+8} & = &-15 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -8x-x& = &-15-8 \\\Leftrightarrow & -9x& = &-23 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-23}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{23}{9} & & \\ & V = \left\{ \frac{23}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-6x-6)& = & -15 \color{red}{-} (2+x) \\\Leftrightarrow & -30x-30& = &-15-2-x \\\Leftrightarrow & -30x \color{red}{-30} & = &-17 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & -30x+x& = &-17+30 \\\Leftrightarrow & -29x& = &13 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{13}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-13}{29} & & \\ & V = \left\{ \frac{-13}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-x+4)& = & 8 \color{red}{-} (-10-2x) \\\Leftrightarrow & -3x+12& = &8+10+2x \\\Leftrightarrow & -3x \color{red}{+12} & = &18 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{+12} \color{blue}{-12} \color{blue}{-2x} & = &18 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-12} \\\Leftrightarrow & -3x-2x& = &18-12 \\\Leftrightarrow & -5x& = &6 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{6}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-6}{5} & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-5x-4)& = & 1 \color{red}{-} (15+x) \\\Leftrightarrow & -30x-24& = &1-15-x \\\Leftrightarrow & -30x \color{red}{-24} & = &-14 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -30x+x& = &-14+24 \\\Leftrightarrow & -29x& = &10 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{10}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-10}{29} & & \\ & V = \left\{ \frac{-10}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (x-3)& = & 1 \color{red}{+} (-7+4x) \\\Leftrightarrow & 3x-9& = &1-7+4x \\\Leftrightarrow & 3x \color{red}{-9} & = &-6 \color{red}{+4x} \\\Leftrightarrow & 3x \color{red}{-9} \color{blue}{+9} \color{blue}{-4x} & = &-6 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+9} \\\Leftrightarrow & 3x-4x& = &-6+9 \\\Leftrightarrow & -x& = &3 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{3}{ \color{red}{-1} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (2x-1)& = & -7 \color{red}{-} (-15-5x) \\\Leftrightarrow & 6x-3& = &-7+15+5x \\\Leftrightarrow & 6x \color{red}{-3} & = &8 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-3} \color{blue}{+3} \color{blue}{-5x} & = &8 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+3} \\\Leftrightarrow & 6x-5x& = &8+3 \\\Leftrightarrow & x& = &11 \\ & V = \left\{ 11 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-x+3)& = & 14 \color{red}{+} (-10-2x) \\\Leftrightarrow & -5x+15& = &14-10-2x \\\Leftrightarrow & -5x \color{red}{+15} & = &4 \color{red}{-2x} \\\Leftrightarrow & -5x \color{red}{+15} \color{blue}{-15} \color{blue}{+2x} & = &4 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-15} \\\Leftrightarrow & -5x+2x& = &4-15 \\\Leftrightarrow & -3x& = &-11 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-11}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{11}{3} & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (6x-1)& = & 11 \color{red}{+} (-12+x) \\\Leftrightarrow & 12x-2& = &11-12+x \\\Leftrightarrow & 12x \color{red}{-2} & = &-1 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & 12x-x& = &-1+2 \\\Leftrightarrow & 11x& = &1 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{1}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{1}{11} & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (6x-7)& = & 4 \color{red}{+} (2+x) \\\Leftrightarrow & 30x-35& = &4+2+x \\\Leftrightarrow & 30x \color{red}{-35} & = &6 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-35} \color{blue}{+35} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+35} \\\Leftrightarrow & 30x-x& = &6+35 \\\Leftrightarrow & 29x& = &41 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{41}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{41}{29} & & \\ & V = \left\{ \frac{41}{29} \right\} & \\\end{align}\)