Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{5}{11})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -9x-\frac{15}{11}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-891}{ \color{blue}{99} }x- \frac{135}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -891x \color{red}{-135} & = & \color{red}{-693x} +110 \\\Leftrightarrow & -891x \color{red}{-135} \color{blue}{+135} \color{blue}{+693x} & = & \color{red}{-693x} +110 \color{blue}{+693x} \color{blue}{+135} \\\Leftrightarrow & -891x+693x& = & 110+135 \\\Leftrightarrow & \color{red}{-198} x& = & 245 \\\Leftrightarrow & x = \frac{245}{-198} & & \\\Leftrightarrow & x = \frac{-245}{198} & & \\ & V = \left\{ \frac{-245}{198} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{4}{7})& = & 4x+\frac{4}{3} \\\Leftrightarrow & 25x+\frac{20}{7}& = & 4x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{525}{ \color{blue}{21} }x+ \frac{60}{ \color{blue}{21} })& = & (\frac{84}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 525x \color{red}{+60} & = & \color{red}{84x} +28 \\\Leftrightarrow & 525x \color{red}{+60} \color{blue}{-60} \color{blue}{-84x} & = & \color{red}{84x} +28 \color{blue}{-84x} \color{blue}{-60} \\\Leftrightarrow & 525x-84x& = & 28-60 \\\Leftrightarrow & \color{red}{441} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{441} & & \\ & V = \left\{ \frac{-32}{441} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{3}{8})& = & 8x+\frac{7}{9} \\\Leftrightarrow & -21x-\frac{21}{8}& = & 8x+\frac{7}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1512}{ \color{blue}{72} }x- \frac{189}{ \color{blue}{72} })& = & (\frac{576}{ \color{blue}{72} }x+ \frac{56}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1512x \color{red}{-189} & = & \color{red}{576x} +56 \\\Leftrightarrow & -1512x \color{red}{-189} \color{blue}{+189} \color{blue}{-576x} & = & \color{red}{576x} +56 \color{blue}{-576x} \color{blue}{+189} \\\Leftrightarrow & -1512x-576x& = & 56+189 \\\Leftrightarrow & \color{red}{-2088} x& = & 245 \\\Leftrightarrow & x = \frac{245}{-2088} & & \\\Leftrightarrow & x = \frac{-245}{2088} & & \\ & V = \left\{ \frac{-245}{2088} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{3}{5})& = & -3x+\frac{2}{3} \\\Leftrightarrow & 8x+\frac{12}{5}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{+36} & = & \color{red}{-45x} +10 \\\Leftrightarrow & 120x \color{red}{+36} \color{blue}{-36} \color{blue}{+45x} & = & \color{red}{-45x} +10 \color{blue}{+45x} \color{blue}{-36} \\\Leftrightarrow & 120x+45x& = & 10-36 \\\Leftrightarrow & \color{red}{165} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{165} & & \\ & V = \left\{ \frac{-26}{165} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{5}{6})& = & -9x+\frac{4}{3} \\\Leftrightarrow & 28x-\frac{35}{6}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{168}{ \color{blue}{6} }x- \frac{35}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 168x \color{red}{-35} & = & \color{red}{-54x} +8 \\\Leftrightarrow & 168x \color{red}{-35} \color{blue}{+35} \color{blue}{+54x} & = & \color{red}{-54x} +8 \color{blue}{+54x} \color{blue}{+35} \\\Leftrightarrow & 168x+54x& = & 8+35 \\\Leftrightarrow & \color{red}{222} x& = & 43 \\\Leftrightarrow & x = \frac{43}{222} & & \\ & V = \left\{ \frac{43}{222} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{3}{7})& = & -3x+\frac{3}{8} \\\Leftrightarrow & 20x-\frac{15}{7}& = & -3x+\frac{3}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1120}{ \color{blue}{56} }x- \frac{120}{ \color{blue}{56} })& = & (\frac{-168}{ \color{blue}{56} }x+ \frac{21}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1120x \color{red}{-120} & = & \color{red}{-168x} +21 \\\Leftrightarrow & 1120x \color{red}{-120} \color{blue}{+120} \color{blue}{+168x} & = & \color{red}{-168x} +21 \color{blue}{+168x} \color{blue}{+120} \\\Leftrightarrow & 1120x+168x& = & 21+120 \\\Leftrightarrow & \color{red}{1288} x& = & 141 \\\Leftrightarrow & x = \frac{141}{1288} & & \\ & V = \left\{ \frac{141}{1288} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{5}{7})& = & -5x+\frac{3}{4} \\\Leftrightarrow & 12x-\frac{20}{7}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{336}{ \color{blue}{28} }x- \frac{80}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 336x \color{red}{-80} & = & \color{red}{-140x} +21 \\\Leftrightarrow & 336x \color{red}{-80} \color{blue}{+80} \color{blue}{+140x} & = & \color{red}{-140x} +21 \color{blue}{+140x} \color{blue}{+80} \\\Leftrightarrow & 336x+140x& = & 21+80 \\\Leftrightarrow & \color{red}{476} x& = & 101 \\\Leftrightarrow & x = \frac{101}{476} & & \\ & V = \left\{ \frac{101}{476} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{4}{5})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 9x+\frac{12}{5}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{135}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 135x \color{red}{+36} & = & \color{red}{-105x} +50 \\\Leftrightarrow & 135x \color{red}{+36} \color{blue}{-36} \color{blue}{+105x} & = & \color{red}{-105x} +50 \color{blue}{+105x} \color{blue}{-36} \\\Leftrightarrow & 135x+105x& = & 50-36 \\\Leftrightarrow & \color{red}{240} x& = & 14 \\\Leftrightarrow & x = \frac{14}{240} & & \\\Leftrightarrow & x = \frac{7}{120} & & \\ & V = \left\{ \frac{7}{120} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{5}{11})& = & -9x+\frac{2}{9} \\\Leftrightarrow & -4x+\frac{10}{11}& = & -9x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-396}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} })& = & (\frac{-891}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -396x \color{red}{+90} & = & \color{red}{-891x} +22 \\\Leftrightarrow & -396x \color{red}{+90} \color{blue}{-90} \color{blue}{+891x} & = & \color{red}{-891x} +22 \color{blue}{+891x} \color{blue}{-90} \\\Leftrightarrow & -396x+891x& = & 22-90 \\\Leftrightarrow & \color{red}{495} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{495} & & \\ & V = \left\{ \frac{-68}{495} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{4}{7})& = & 3x+\frac{3}{2} \\\Leftrightarrow & 16x+\frac{16}{7}& = & 3x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{224}{ \color{blue}{14} }x+ \frac{32}{ \color{blue}{14} })& = & (\frac{42}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 224x \color{red}{+32} & = & \color{red}{42x} +21 \\\Leftrightarrow & 224x \color{red}{+32} \color{blue}{-32} \color{blue}{-42x} & = & \color{red}{42x} +21 \color{blue}{-42x} \color{blue}{-32} \\\Leftrightarrow & 224x-42x& = & 21-32 \\\Leftrightarrow & \color{red}{182} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{182} & & \\ & V = \left\{ \frac{-11}{182} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{3}{5})& = & 9x+\frac{5}{9} \\\Leftrightarrow & -18x+\frac{18}{5}& = & 9x+\frac{5}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-810}{ \color{blue}{45} }x+ \frac{162}{ \color{blue}{45} })& = & (\frac{405}{ \color{blue}{45} }x+ \frac{25}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -810x \color{red}{+162} & = & \color{red}{405x} +25 \\\Leftrightarrow & -810x \color{red}{+162} \color{blue}{-162} \color{blue}{-405x} & = & \color{red}{405x} +25 \color{blue}{-405x} \color{blue}{-162} \\\Leftrightarrow & -810x-405x& = & 25-162 \\\Leftrightarrow & \color{red}{-1215} x& = & -137 \\\Leftrightarrow & x = \frac{-137}{-1215} & & \\\Leftrightarrow & x = \frac{137}{1215} & & \\ & V = \left\{ \frac{137}{1215} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{3}{5})& = & 3x+\frac{5}{4} \\\Leftrightarrow & 8x+\frac{12}{5}& = & 3x+\frac{5}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{160}{ \color{blue}{20} }x+ \frac{48}{ \color{blue}{20} })& = & (\frac{60}{ \color{blue}{20} }x+ \frac{25}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 160x \color{red}{+48} & = & \color{red}{60x} +25 \\\Leftrightarrow & 160x \color{red}{+48} \color{blue}{-48} \color{blue}{-60x} & = & \color{red}{60x} +25 \color{blue}{-60x} \color{blue}{-48} \\\Leftrightarrow & 160x-60x& = & 25-48 \\\Leftrightarrow & \color{red}{100} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{100} & & \\ & V = \left\{ \frac{-23}{100} \right\} & \\\end{align}\)