Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{4}{9})& = & 3x+\frac{6}{7} \\\Leftrightarrow & -25x+\frac{20}{9}& = & 3x+\frac{6}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1575}{ \color{blue}{63} }x+ \frac{140}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1575x \color{red}{+140} & = & \color{red}{189x} +54 \\\Leftrightarrow & -1575x \color{red}{+140} \color{blue}{-140} \color{blue}{-189x} & = & \color{red}{189x} +54 \color{blue}{-189x} \color{blue}{-140} \\\Leftrightarrow & -1575x-189x& = & 54-140 \\\Leftrightarrow & \color{red}{-1764} x& = & -86 \\\Leftrightarrow & x = \frac{-86}{-1764} & & \\\Leftrightarrow & x = \frac{43}{882} & & \\ & V = \left\{ \frac{43}{882} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{4}{5})& = & -8x+\frac{4}{5} \\\Leftrightarrow & -15x-\frac{12}{5}& = & -8x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-75}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-40}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -75x \color{red}{-12} & = & \color{red}{-40x} +4 \\\Leftrightarrow & -75x \color{red}{-12} \color{blue}{+12} \color{blue}{+40x} & = & \color{red}{-40x} +4 \color{blue}{+40x} \color{blue}{+12} \\\Leftrightarrow & -75x+40x& = & 4+12 \\\Leftrightarrow & \color{red}{-35} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-35} & & \\\Leftrightarrow & x = \frac{-16}{35} & & \\ & V = \left\{ \frac{-16}{35} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{3}{8})& = & -4x+\frac{5}{6} \\\Leftrightarrow & 21x-\frac{21}{8}& = & -4x+\frac{5}{6} \\ & & & \text{kgv van noemers 8 en 6 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{504}{ \color{blue}{24} }x- \frac{63}{ \color{blue}{24} })& = & (\frac{-96}{ \color{blue}{24} }x+ \frac{20}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 504x \color{red}{-63} & = & \color{red}{-96x} +20 \\\Leftrightarrow & 504x \color{red}{-63} \color{blue}{+63} \color{blue}{+96x} & = & \color{red}{-96x} +20 \color{blue}{+96x} \color{blue}{+63} \\\Leftrightarrow & 504x+96x& = & 20+63 \\\Leftrightarrow & \color{red}{600} x& = & 83 \\\Leftrightarrow & x = \frac{83}{600} & & \\ & V = \left\{ \frac{83}{600} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{5}{9})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -6x-\frac{10}{9}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-54}{ \color{blue}{9} }x- \frac{10}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -54x \color{red}{-10} & = & \color{red}{-63x} +12 \\\Leftrightarrow & -54x \color{red}{-10} \color{blue}{+10} \color{blue}{+63x} & = & \color{red}{-63x} +12 \color{blue}{+63x} \color{blue}{+10} \\\Leftrightarrow & -54x+63x& = & 12+10 \\\Leftrightarrow & \color{red}{9} x& = & 22 \\\Leftrightarrow & x = \frac{22}{9} & & \\ & V = \left\{ \frac{22}{9} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{3}{7})& = & 3x+\frac{4}{3} \\\Leftrightarrow & -18x-\frac{18}{7}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-378}{ \color{blue}{21} }x- \frac{54}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -378x \color{red}{-54} & = & \color{red}{63x} +28 \\\Leftrightarrow & -378x \color{red}{-54} \color{blue}{+54} \color{blue}{-63x} & = & \color{red}{63x} +28 \color{blue}{-63x} \color{blue}{+54} \\\Leftrightarrow & -378x-63x& = & 28+54 \\\Leftrightarrow & \color{red}{-441} x& = & 82 \\\Leftrightarrow & x = \frac{82}{-441} & & \\\Leftrightarrow & x = \frac{-82}{441} & & \\ & V = \left\{ \frac{-82}{441} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{4}{3})& = & 4x+\frac{9}{2} \\\Leftrightarrow & 15x+\frac{20}{3}& = & 4x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{90}{ \color{blue}{6} }x+ \frac{40}{ \color{blue}{6} })& = & (\frac{24}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 90x \color{red}{+40} & = & \color{red}{24x} +27 \\\Leftrightarrow & 90x \color{red}{+40} \color{blue}{-40} \color{blue}{-24x} & = & \color{red}{24x} +27 \color{blue}{-24x} \color{blue}{-40} \\\Leftrightarrow & 90x-24x& = & 27-40 \\\Leftrightarrow & \color{red}{66} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{66} & & \\ & V = \left\{ \frac{-13}{66} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{5}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 30x+\frac{30}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{1050}{ \color{blue}{35} }x+ \frac{150}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 1050x \color{red}{+150} & = & \color{red}{-245x} +42 \\\Leftrightarrow & 1050x \color{red}{+150} \color{blue}{-150} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{-150} \\\Leftrightarrow & 1050x+245x& = & 42-150 \\\Leftrightarrow & \color{red}{1295} x& = & -108 \\\Leftrightarrow & x = \frac{-108}{1295} & & \\ & V = \left\{ \frac{-108}{1295} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{5}{6})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 20x-\frac{25}{6}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{120}{ \color{blue}{6} }x- \frac{25}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 120x \color{red}{-25} & = & \color{red}{42x} +8 \\\Leftrightarrow & 120x \color{red}{-25} \color{blue}{+25} \color{blue}{-42x} & = & \color{red}{42x} +8 \color{blue}{-42x} \color{blue}{+25} \\\Leftrightarrow & 120x-42x& = & 8+25 \\\Leftrightarrow & \color{red}{78} x& = & 33 \\\Leftrightarrow & x = \frac{33}{78} & & \\\Leftrightarrow & x = \frac{11}{26} & & \\ & V = \left\{ \frac{11}{26} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{4}{5})& = & -7x+\frac{9}{2} \\\Leftrightarrow & 8x-\frac{16}{5}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{80}{ \color{blue}{10} }x- \frac{32}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 80x \color{red}{-32} & = & \color{red}{-70x} +45 \\\Leftrightarrow & 80x \color{red}{-32} \color{blue}{+32} \color{blue}{+70x} & = & \color{red}{-70x} +45 \color{blue}{+70x} \color{blue}{+32} \\\Leftrightarrow & 80x+70x& = & 45+32 \\\Leftrightarrow & \color{red}{150} x& = & 77 \\\Leftrightarrow & x = \frac{77}{150} & & \\ & V = \left\{ \frac{77}{150} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{5}{3})& = & 7x+\frac{3}{7} \\\Leftrightarrow & -16x-\frac{20}{3}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-336}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{9}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -336x \color{red}{-140} & = & \color{red}{147x} +9 \\\Leftrightarrow & -336x \color{red}{-140} \color{blue}{+140} \color{blue}{-147x} & = & \color{red}{147x} +9 \color{blue}{-147x} \color{blue}{+140} \\\Leftrightarrow & -336x-147x& = & 9+140 \\\Leftrightarrow & \color{red}{-483} x& = & 149 \\\Leftrightarrow & x = \frac{149}{-483} & & \\\Leftrightarrow & x = \frac{-149}{483} & & \\ & V = \left\{ \frac{-149}{483} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{3}{11})& = & -7x+\frac{2}{7} \\\Leftrightarrow & -24x-\frac{18}{11}& = & -7x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1848}{ \color{blue}{77} }x- \frac{126}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1848x \color{red}{-126} & = & \color{red}{-539x} +22 \\\Leftrightarrow & -1848x \color{red}{-126} \color{blue}{+126} \color{blue}{+539x} & = & \color{red}{-539x} +22 \color{blue}{+539x} \color{blue}{+126} \\\Leftrightarrow & -1848x+539x& = & 22+126 \\\Leftrightarrow & \color{red}{-1309} x& = & 148 \\\Leftrightarrow & x = \frac{148}{-1309} & & \\\Leftrightarrow & x = \frac{-148}{1309} & & \\ & V = \left\{ \frac{-148}{1309} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{5}{7})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -30x-\frac{30}{7}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-210}{ \color{blue}{7} }x- \frac{30}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -210x \color{red}{-30} & = & \color{red}{-49x} +10 \\\Leftrightarrow & -210x \color{red}{-30} \color{blue}{+30} \color{blue}{+49x} & = & \color{red}{-49x} +10 \color{blue}{+49x} \color{blue}{+30} \\\Leftrightarrow & -210x+49x& = & 10+30 \\\Leftrightarrow & \color{red}{-161} x& = & 40 \\\Leftrightarrow & x = \frac{40}{-161} & & \\\Leftrightarrow & x = \frac{-40}{161} & & \\ & V = \left\{ \frac{-40}{161} \right\} & \\\end{align}\)