Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{5}{4})& = & 5x+\frac{9}{8} \\\Leftrightarrow & 12x-\frac{15}{4}& = & 5x+\frac{9}{8} \\ & & & \text{kgv van noemers 4 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{96}{ \color{blue}{8} }x- \frac{30}{ \color{blue}{8} })& = & (\frac{40}{ \color{blue}{8} }x+ \frac{9}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 96x \color{red}{-30} & = & \color{red}{40x} +9 \\\Leftrightarrow & 96x \color{red}{-30} \color{blue}{+30} \color{blue}{-40x} & = & \color{red}{40x} +9 \color{blue}{-40x} \color{blue}{+30} \\\Leftrightarrow & 96x-40x& = & 9+30 \\\Leftrightarrow & \color{red}{56} x& = & 39 \\\Leftrightarrow & x = \frac{39}{56} & & \\ & V = \left\{ \frac{39}{56} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{5}{9})& = & -8x+\frac{7}{8} \\\Leftrightarrow & -15x+\frac{25}{9}& = & -8x+\frac{7}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1080}{ \color{blue}{72} }x+ \frac{200}{ \color{blue}{72} })& = & (\frac{-576}{ \color{blue}{72} }x+ \frac{63}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1080x \color{red}{+200} & = & \color{red}{-576x} +63 \\\Leftrightarrow & -1080x \color{red}{+200} \color{blue}{-200} \color{blue}{+576x} & = & \color{red}{-576x} +63 \color{blue}{+576x} \color{blue}{-200} \\\Leftrightarrow & -1080x+576x& = & 63-200 \\\Leftrightarrow & \color{red}{-504} x& = & -137 \\\Leftrightarrow & x = \frac{-137}{-504} & & \\\Leftrightarrow & x = \frac{137}{504} & & \\ & V = \left\{ \frac{137}{504} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{3}{11})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -24x-\frac{18}{11}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1320}{ \color{blue}{55} }x- \frac{90}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1320x \color{red}{-90} & = & \color{red}{-275x} +66 \\\Leftrightarrow & -1320x \color{red}{-90} \color{blue}{+90} \color{blue}{+275x} & = & \color{red}{-275x} +66 \color{blue}{+275x} \color{blue}{+90} \\\Leftrightarrow & -1320x+275x& = & 66+90 \\\Leftrightarrow & \color{red}{-1045} x& = & 156 \\\Leftrightarrow & x = \frac{156}{-1045} & & \\\Leftrightarrow & x = \frac{-156}{1045} & & \\ & V = \left\{ \frac{-156}{1045} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{4}{11})& = & 2x+\frac{5}{2} \\\Leftrightarrow & 15x+\frac{12}{11}& = & 2x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{330}{ \color{blue}{22} }x+ \frac{24}{ \color{blue}{22} })& = & (\frac{44}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 330x \color{red}{+24} & = & \color{red}{44x} +55 \\\Leftrightarrow & 330x \color{red}{+24} \color{blue}{-24} \color{blue}{-44x} & = & \color{red}{44x} +55 \color{blue}{-44x} \color{blue}{-24} \\\Leftrightarrow & 330x-44x& = & 55-24 \\\Leftrightarrow & \color{red}{286} x& = & 31 \\\Leftrightarrow & x = \frac{31}{286} & & \\ & V = \left\{ \frac{31}{286} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{5}{7})& = & -9x+\frac{4}{5} \\\Leftrightarrow & -8x-\frac{10}{7}& = & -9x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{-50} & = & \color{red}{-315x} +28 \\\Leftrightarrow & -280x \color{red}{-50} \color{blue}{+50} \color{blue}{+315x} & = & \color{red}{-315x} +28 \color{blue}{+315x} \color{blue}{+50} \\\Leftrightarrow & -280x+315x& = & 28+50 \\\Leftrightarrow & \color{red}{35} x& = & 78 \\\Leftrightarrow & x = \frac{78}{35} & & \\ & V = \left\{ \frac{78}{35} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{2}{7})& = & 9x+\frac{4}{3} \\\Leftrightarrow & -20x+\frac{10}{7}& = & 9x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{+30} & = & \color{red}{189x} +28 \\\Leftrightarrow & -420x \color{red}{+30} \color{blue}{-30} \color{blue}{-189x} & = & \color{red}{189x} +28 \color{blue}{-189x} \color{blue}{-30} \\\Leftrightarrow & -420x-189x& = & 28-30 \\\Leftrightarrow & \color{red}{-609} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-609} & & \\\Leftrightarrow & x = \frac{2}{609} & & \\ & V = \left\{ \frac{2}{609} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{2}{11})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -30x-\frac{12}{11}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-990}{ \color{blue}{33} }x- \frac{36}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -990x \color{red}{-36} & = & \color{red}{231x} +88 \\\Leftrightarrow & -990x \color{red}{-36} \color{blue}{+36} \color{blue}{-231x} & = & \color{red}{231x} +88 \color{blue}{-231x} \color{blue}{+36} \\\Leftrightarrow & -990x-231x& = & 88+36 \\\Leftrightarrow & \color{red}{-1221} x& = & 124 \\\Leftrightarrow & x = \frac{124}{-1221} & & \\\Leftrightarrow & x = \frac{-124}{1221} & & \\ & V = \left\{ \frac{-124}{1221} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{4}{9})& = & 3x+\frac{4}{3} \\\Leftrightarrow & -20x+\frac{20}{9}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-180}{ \color{blue}{9} }x+ \frac{20}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -180x \color{red}{+20} & = & \color{red}{27x} +12 \\\Leftrightarrow & -180x \color{red}{+20} \color{blue}{-20} \color{blue}{-27x} & = & \color{red}{27x} +12 \color{blue}{-27x} \color{blue}{-20} \\\Leftrightarrow & -180x-27x& = & 12-20 \\\Leftrightarrow & \color{red}{-207} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-207} & & \\\Leftrightarrow & x = \frac{8}{207} & & \\ & V = \left\{ \frac{8}{207} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{4}{3})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -10x+\frac{20}{3}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{+140} & = & \color{red}{147x} +27 \\\Leftrightarrow & -210x \color{red}{+140} \color{blue}{-140} \color{blue}{-147x} & = & \color{red}{147x} +27 \color{blue}{-147x} \color{blue}{-140} \\\Leftrightarrow & -210x-147x& = & 27-140 \\\Leftrightarrow & \color{red}{-357} x& = & -113 \\\Leftrightarrow & x = \frac{-113}{-357} & & \\\Leftrightarrow & x = \frac{113}{357} & & \\ & V = \left\{ \frac{113}{357} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{5}{7})& = & -3x+\frac{7}{2} \\\Leftrightarrow & 8x+\frac{10}{7}& = & -3x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{112}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} })& = & (\frac{-42}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 112x \color{red}{+20} & = & \color{red}{-42x} +49 \\\Leftrightarrow & 112x \color{red}{+20} \color{blue}{-20} \color{blue}{+42x} & = & \color{red}{-42x} +49 \color{blue}{+42x} \color{blue}{-20} \\\Leftrightarrow & 112x+42x& = & 49-20 \\\Leftrightarrow & \color{red}{154} x& = & 29 \\\Leftrightarrow & x = \frac{29}{154} & & \\ & V = \left\{ \frac{29}{154} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{5}{7})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 30x+\frac{30}{7}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{630}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 630x \color{red}{+90} & = & \color{red}{147x} +70 \\\Leftrightarrow & 630x \color{red}{+90} \color{blue}{-90} \color{blue}{-147x} & = & \color{red}{147x} +70 \color{blue}{-147x} \color{blue}{-90} \\\Leftrightarrow & 630x-147x& = & 70-90 \\\Leftrightarrow & \color{red}{483} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{483} & & \\ & V = \left\{ \frac{-20}{483} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{2}{7})& = & -4x+\frac{3}{2} \\\Leftrightarrow & -15x-\frac{6}{7}& = & -4x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-210}{ \color{blue}{14} }x- \frac{12}{ \color{blue}{14} })& = & (\frac{-56}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -210x \color{red}{-12} & = & \color{red}{-56x} +21 \\\Leftrightarrow & -210x \color{red}{-12} \color{blue}{+12} \color{blue}{+56x} & = & \color{red}{-56x} +21 \color{blue}{+56x} \color{blue}{+12} \\\Leftrightarrow & -210x+56x& = & 21+12 \\\Leftrightarrow & \color{red}{-154} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-154} & & \\\Leftrightarrow & x = \frac{-3}{14} & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)