Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (2x-2)& = & 15 \color{red}{+} (-11+3x) \\\Leftrightarrow & 8x-8& = &15-11+3x \\\Leftrightarrow & 8x \color{red}{-8} & = &4 \color{red}{+3x} \\\Leftrightarrow & 8x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &4 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & 8x-3x& = &4+8 \\\Leftrightarrow & 5x& = &12 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{12}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{12}{5} & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-5x+5)& = & 10 \color{red}{+} (-13+x) \\\Leftrightarrow & -20x+20& = &10-13+x \\\Leftrightarrow & -20x \color{red}{+20} & = &-3 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -20x-x& = &-3-20 \\\Leftrightarrow & -21x& = &-23 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-23}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{23}{21} & & \\ & V = \left\{ \frac{23}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (3x+5)& = & -11 \color{red}{+} (-14-2x) \\\Leftrightarrow & 9x+15& = &-11-14-2x \\\Leftrightarrow & 9x \color{red}{+15} & = &-25 \color{red}{-2x} \\\Leftrightarrow & 9x \color{red}{+15} \color{blue}{-15} \color{blue}{+2x} & = &-25 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-15} \\\Leftrightarrow & 9x+2x& = &-25-15 \\\Leftrightarrow & 11x& = &-40 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-40}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-40}{11} & & \\ & V = \left\{ \frac{-40}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-5x-4)& = & 12 \color{red}{+} (9-4x) \\\Leftrightarrow & -25x-20& = &12+9-4x \\\Leftrightarrow & -25x \color{red}{-20} & = &21 \color{red}{-4x} \\\Leftrightarrow & -25x \color{red}{-20} \color{blue}{+20} \color{blue}{+4x} & = &21 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+20} \\\Leftrightarrow & -25x+4x& = &21+20 \\\Leftrightarrow & -21x& = &41 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{41}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-41}{21} & & \\ & V = \left\{ \frac{-41}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-3x+3)& = & 9 \color{red}{+} (10-4x) \\\Leftrightarrow & -9x+9& = &9+10-4x \\\Leftrightarrow & -9x \color{red}{+9} & = &19 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{+9} \color{blue}{-9} \color{blue}{+4x} & = &19 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-9} \\\Leftrightarrow & -9x+4x& = &19-9 \\\Leftrightarrow & -5x& = &10 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{10}{ \color{red}{-5} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (5x+3)& = & -3 \color{red}{+} (-8+x) \\\Leftrightarrow & 30x+18& = &-3-8+x \\\Leftrightarrow & 30x \color{red}{+18} & = &-11 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 30x-x& = &-11-18 \\\Leftrightarrow & 29x& = &-29 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-29}{ \color{red}{29} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (3x-1)& = & 3 \color{red}{+} (15+x) \\\Leftrightarrow & 6x-2& = &3+15+x \\\Leftrightarrow & 6x \color{red}{-2} & = &18 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & 6x-x& = &18+2 \\\Leftrightarrow & 5x& = &20 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{20}{ \color{red}{5} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-2x+2)& = & -6 \color{red}{-} (-8+x) \\\Leftrightarrow & -12x+12& = &-6+8-x \\\Leftrightarrow & -12x \color{red}{+12} & = &2 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -12x+x& = &2-12 \\\Leftrightarrow & -11x& = &-10 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-10}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{10}{11} & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (2x-5)& = & 5 \color{red}{+} (7-3x) \\\Leftrightarrow & 4x-10& = &5+7-3x \\\Leftrightarrow & 4x \color{red}{-10} & = &12 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &12 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & 4x+3x& = &12+10 \\\Leftrightarrow & 7x& = &22 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{22}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{22}{7} & & \\ & V = \left\{ \frac{22}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (4x+5)& = & -15 \color{red}{-} (7-5x) \\\Leftrightarrow & 16x+20& = &-15-7+5x \\\Leftrightarrow & 16x \color{red}{+20} & = &-22 \color{red}{+5x} \\\Leftrightarrow & 16x \color{red}{+20} \color{blue}{-20} \color{blue}{-5x} & = &-22 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-20} \\\Leftrightarrow & 16x-5x& = &-22-20 \\\Leftrightarrow & 11x& = &-42 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-42}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-42}{11} & & \\ & V = \left\{ \frac{-42}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-6x+5)& = & -2 \color{red}{-} (-4+x) \\\Leftrightarrow & -12x+10& = &-2+4-x \\\Leftrightarrow & -12x \color{red}{+10} & = &2 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -12x+x& = &2-10 \\\Leftrightarrow & -11x& = &-8 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-8}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{8}{11} & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (3x-7)& = & 9 \color{red}{+} (-12+x) \\\Leftrightarrow & 12x-28& = &9-12+x \\\Leftrightarrow & 12x \color{red}{-28} & = &-3 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & 12x-x& = &-3+28 \\\Leftrightarrow & 11x& = &25 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{25}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{25}{11} & & \\ & V = \left\{ \frac{25}{11} \right\} & \\\end{align}\)