Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-2x-5)& = & 15 \color{red}{+} (-10+x) \\\Leftrightarrow & -4x-10& = &15-10+x \\\Leftrightarrow & -4x \color{red}{-10} & = &5 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -4x-x& = &5+10 \\\Leftrightarrow & -5x& = &15 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{15}{ \color{red}{-5} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-3x-7)& = & -2 \color{red}{-} (-9+x) \\\Leftrightarrow & -6x-14& = &-2+9-x \\\Leftrightarrow & -6x \color{red}{-14} & = &7 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & -6x+x& = &7+14 \\\Leftrightarrow & -5x& = &21 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{21}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-21}{5} & & \\ & V = \left\{ \frac{-21}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-3x-5)& = & 12 \color{red}{+} (15+x) \\\Leftrightarrow & -18x-30& = &12+15+x \\\Leftrightarrow & -18x \color{red}{-30} & = &27 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &27 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -18x-x& = &27+30 \\\Leftrightarrow & -19x& = &57 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{57}{ \color{red}{-19} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (6x-6)& = & 12 \color{red}{+} (14+x) \\\Leftrightarrow & 30x-30& = &12+14+x \\\Leftrightarrow & 30x \color{red}{-30} & = &26 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &26 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 30x-x& = &26+30 \\\Leftrightarrow & 29x& = &56 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{56}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{56}{29} & & \\ & V = \left\{ \frac{56}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-x-5)& = & -9 \color{red}{-} (-8+x) \\\Leftrightarrow & -2x-10& = &-9+8-x \\\Leftrightarrow & -2x \color{red}{-10} & = &-1 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -2x+x& = &-1+10 \\\Leftrightarrow & -x& = &9 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{9}{ \color{red}{-1} } \\\Leftrightarrow & x = -9 & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (2x-5)& = & 14 \color{red}{+} (15-3x) \\\Leftrightarrow & 4x-10& = &14+15-3x \\\Leftrightarrow & 4x \color{red}{-10} & = &29 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &29 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & 4x+3x& = &29+10 \\\Leftrightarrow & 7x& = &39 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{39}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{39}{7} & & \\ & V = \left\{ \frac{39}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-2x-5)& = & -2 \color{red}{+} (5+x) \\\Leftrightarrow & -10x-25& = &-2+5+x \\\Leftrightarrow & -10x \color{red}{-25} & = &3 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-25} \color{blue}{+25} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{+25} \\\Leftrightarrow & -10x-x& = &3+25 \\\Leftrightarrow & -11x& = &28 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{28}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-28}{11} & & \\ & V = \left\{ \frac{-28}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-4x+4)& = & -1 \color{red}{+} (3+x) \\\Leftrightarrow & -20x+20& = &-1+3+x \\\Leftrightarrow & -20x \color{red}{+20} & = &2 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -20x-x& = &2-20 \\\Leftrightarrow & -21x& = &-18 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-18}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{6}{7} & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (4x-1)& = & -13 \color{red}{-} (-15+3x) \\\Leftrightarrow & 8x-2& = &-13+15-3x \\\Leftrightarrow & 8x \color{red}{-2} & = &2 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{-2} \color{blue}{+2} \color{blue}{+3x} & = &2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+2} \\\Leftrightarrow & 8x+3x& = &2+2 \\\Leftrightarrow & 11x& = &4 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{4}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{4}{11} & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (3x+1)& = & -6 \color{red}{+} (-2+x) \\\Leftrightarrow & 9x+3& = &-6-2+x \\\Leftrightarrow & 9x \color{red}{+3} & = &-8 \color{red}{+x} \\\Leftrightarrow & 9x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & 9x-x& = &-8-3 \\\Leftrightarrow & 8x& = &-11 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{-11}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{-11}{8} & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (x-2)& = & 2 \color{red}{-} (-3+x) \\\Leftrightarrow & 2x-4& = &2+3-x \\\Leftrightarrow & 2x \color{red}{-4} & = &5 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 2x+x& = &5+4 \\\Leftrightarrow & 3x& = &9 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{9}{ \color{red}{3} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (x-6)& = & -4 \color{red}{+} (8+x) \\\Leftrightarrow & 2x-12& = &-4+8+x \\\Leftrightarrow & 2x \color{red}{-12} & = &4 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 2x-x& = &4+12 \\\Leftrightarrow & x& = &16 \\ & V = \left\{ 16 \right\} & \\\end{align}\)